RBSE Class 12 Maths Important Questions Chapter 3 Matrices

Rajasthan Board RBSE Class 12 Maths Important Questions Chapter 3 Matrices Important Questions and Answers.

Rajasthan Board RBSE Solutions for Class 12 Maths in Hindi Medium & English Medium are part of RBSE Solutions for Class 12. Students can also read RBSE Class 12 Maths Important Questions for exam preparation. Students can also go through RBSE Class 12 Maths Notes to understand and remember the concepts easily.

RBSE Class 12 Maths Chapter 3 Important Questions Matrices

Question 1.
If \(\left[\begin{array}{cc} x-y & 2 x+z \\ 2 x-y & 3 z+\omega \end{array}\right]\)= \(\left[\begin{array}{rr} -1 & 5 \\ 0 & 13 \end{array}\right]\) = \(\left[\begin{array}{rr} -1 & 5 \\ 0 & 13 \end{array}\right]\), find x, y, z and w
Answer:
Given, matrix equation is:
\(\left[\begin{array}{cc} x-y & 2 x+z \\ 2 x-y & 3 z+w \end{array}\right]\)= \(\left[\begin{array}{cc} -1 & 5 \\ 0 & 13 \end{array}\right]\)
On equating the corresponding elements, we get
x - y = - 1 ...... (i)
2x - y = 0 ....... (ii)
2x + z = 5 ...... (iii)
3z + w = 13 .......... (iv)
Subtracting eq. (ii), from (i), we get
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 1
Substituting x = 1 in eq. (i), we get
1 - y = - 1
⇒ - y = - 2
⇒ y = 2
Substituting the value of x in Eq. (iii), we get
2 × 1 + z = 5
⇒ z = 5 - 2 = 3
Substituting the value of z in Eq. (iv), we get
3 × 3 + w = 13
⇒ w = 13 - 9
w = 4
Thus, x = 1, y = 2, z = 3, w = 4

RBSE Class 12 Maths Important Questions Chapter 3 Matrices

Question 2.
Construct a 2 × 2 matrix A = [aij] whose elements are given by:
(i) aij = \(\frac{(i-2 j)^2}{2}\)
Answer:
Matrix of order 2 × 2 will be as follows:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 2

(ii) aij = \(\frac{(2 i+j)^2}{2}\)
Answer:
Since, it is a 2 × 2 matrix, it has 2 rows and 2 columns.
Let the matrix be A,
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 3

Question 3.
If \(\left[\begin{array}{cc} x-y & z \\ 2 x-y & w \end{array}\right]\) = \(\left[\begin{array}{rr} -1 & 4 \\ 0 & 5 \end{array}\right]\), find x, y, z and w.
Answer:
Given, matrix equation is:
\(\left[\begin{array}{cc} x-y & z \\ 2 x-y & w \end{array}\right]\) = \(\left[\begin{array}{cc} -1 & 4 \\ 0 & 5 \end{array}\right]\)
On equating the corresponding elements, we get
x - y = - 1 ...... (i)
2x - y = 0 ....... (ii)
z = 4 ........ (iii)
w = 5 ........ (iv)
Subtracting equation (ii), from (j), we get
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 4
Substituting the value of x in Eq. (ii), we get
y = 2
Thus, x = 1, y = 2, z = 4 and w = 5

RBSE Class 12 Maths Important Questions Chapter 3 Matrices

Question 4.
If \(\left[\begin{array}{cc} 2 x+1 & 5 x \\ 0 & y^2+1 \end{array}\right]\) = \(\left[\begin{array}{cc} x+3 & 10 \\ 0 & 26 \end{array}\right]\), find the value of (x + y).
Answer:
Given, matrix equation is:
\(\left[\begin{array}{cc} 2 x+1 & 5 x \\ 0 & y^2+1 \end{array}\right]\) = \(\left[\begin{array}{cc} x+3 & 10 \\ 0 & 26 \end{array}\right]\)
On equating the corresponding elements, we get
2x + 1 = x + 3
⇒ x = 2
And y2 + 1 = 26
⇒ y2 = 26 - 1 = 25
⇒ y = ±5
If y = + 5, then x + y = 2 + 5 = 7
and if y= - 5, then x + y = 2 - 5 = - 3

Question 5.
Construct a 2 × 2 matrix A = [aij] whose elements are given by aij = |(i)2 - j|.
Answer:
Matrix of order 2 × 2 will be as follows:
A = \(\left[\begin{array}{ll} a_{11} & a_{12} \\ a_{22} & a_{23} \end{array}\right]\)
Now, aij = [(i)2 - j]
a11 = (1)2 - 1 = 1 - 1 = 0
a12 = (1)2 - 2 = 1 - 2 = - 1
a21 = (2)2 - 1 = 4 - 1 = 3
a22 = (2)2 - 1 = 4 - 2 = 2
Thus, the matrix of order 2 × 2 is:
A = \(\left[\begin{array}{cc} 0 & -1 \\ 3 & 2 \end{array}\right]\)
then 3A = 3\(\left[\begin{array}{rr} 1 & -3 \\ 0 & 3 \end{array}\right]\) = \(\left[\begin{array}{rr} 3 \times 1 & 3 \times(-3) \\ 3 \times 0 & 3 \times 3 \end{array}\right]\)
= \(\left[\begin{array}{rr} 3 & -9 \\ 0 & 9 \end{array}\right]\)

Question 6.
Find a matrix X such that 2A + B + X = 0, where A = \(\left[\begin{array}{rr} -1 & 2 \\ 3 & 4 \end{array}\right]\) and B = \(\left[\begin{array}{rr} 3 & -2 \\ 1 & 5 \end{array}\right]\).
Answer:
We have
2A + B + X = 0
x = - 2A - B
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 5

Question 7.
Find a matrix A such that 2A - 3B + 5C = 0, where B = \(\left[\begin{array}{rrr} -2 & 2 & 0 \\ 3 & 1 & 4 \end{array}\right]\) and C = \(\left[\begin{array}{rrr} 2 & 0 & -2 \\ 7 & 1 & 6 \end{array}\right]\).
Answer:
We have,
2A - 3B + 5C = 0
2A = 3B - 5C
A = \(\frac{3 B-5 C}{2}\) = \(\frac{3}{2}\)B - \(\frac{5}{2}\)C
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 6

RBSE Class 12 Maths Important Questions Chapter 3 Matrices

Question 8.
The monthly incomes of Aryan and Baban are in the ratio 3 :4 and their monthly expenditures are In the ratio 5 : 7. If each saves ₹ 1500 per month, find their monthly incomes using matrix method. This problem reflects which values.
Answer:
Let the incomes of Aryan and Baban be 3x and 4x respectively. Similarly, their expenditures would be 5y and 7y respectively.
Since, each saves ₹ 1500, we get
3x - 5y = 1500
4x - 7y = 1500
This can be written form as:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 7
∴ x = 3000
Thus, their incomes was 3 × 3000 = ₹ 9,000 and 4 × 3000 = ₹ 12000 respectively.

Question 9.
If A = \(\left[\begin{array}{ll} 1 & -1 \\ 2 & -1 \end{array}\right]\), B = \(\left[\begin{array}{rr} a & 1 \\ b & -1 \end{array}\right]\) and (A + B)2 = A2 + B2, find a and b.
Answer:
We have
(A + B)2 = A2 + B2
⇒ (A + B) (A + B) = A2 + B2
⇒ A2 + BA + AB + B2 + A2 + B2
⇒ BA + AB = 0
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 8
On equating the corresponding elements, we get
⇒ 2a - b + 2 = 0 ......... (i)
- a + 1 = 0 ....... (ii)
2a - 2 = 0 ........ (iii)
- b + 4 = 0 ....... (iv)
On solving these equations, we get
a = 1, b = 4

RBSE Class 12 Maths Important Questions Chapter 3 Matrices

Question 10.
Find the value of x, for the following:
\(\left[\begin{array}{lll} 1 & x & 1 \end{array}\right]\left[\begin{array}{ccc} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{array}\right]\left[\begin{array}{l} 1 \\ 2 \\ x \end{array}\right]\) = 0
Answer:
We have
\(\left[\begin{array}{lll} 1 & x & 1 \end{array}\right]\left[\begin{array}{c} 7+2 x \\ 12+x \\ 21+2 x \end{array}\right]\) = 0
⇒ 7 + 2x + 12x + x2 + 21 + 2x = 0
⇒ x2 + 16x + 28 = 0
⇒ (x + 14) (x + 2) = 0
Either x+ 14 = 0 ⇒ x = - 14
or x + 2 = 0 ⇒ x = - 2

Question 11.
If A is a square matrix such that A2 = 1, then find the simplified value of (A - I)3 + (A + I)3 - 7A.
Answer:
We have, A2 = I
∴ A3 = A2.A = IA = A
We know that
(A + B)3 = A3 + 3A2B + 3AB2 + B2
(A - B)3 = A3 - 3A2B + 3AB2 - B3
Provided that AB = BA
Since AI = IA = A
∴ (A + I)3 = A3 + 3A2I + 3AI2 + I
⇒ (A - I)3 = A3 - 3A2I + 3AI2 - I
∴ (A + I)3 + (A - I)3 = 2(A3 + 3A)
⇒ (A + I)3 × (A - I)3 = 2(A + 3A) [By (i)]
⇒ (A + I)3 + (A - I)3 = 8A
Thus, (A - I)3 + (A + I)3 - 7A
= 8A - 7A = A

Question 12.
Find the matrix A such that
(i) \(\left[\begin{array}{rr} 2 & -1 \\ 1 & 0 \\ -3 & 4 \end{array}\right]\) A = \(\left[\begin{array}{rr} -1 & -8 \\ 1 & -2 \\ 9 & 22 \end{array}\right]\)
Answer:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 9
On equating the corresponding elements, we get
⇒ 2a - c = - 1 ........... (i)
2b - d = - 8 .......... (ii)
a = 1 ......... (iii)
b = - 2 ......... (iv)
- 3a + 4c = 9 .......... (v)
- 3b + 4d = 22 .......... (vi)
On solving these equations, we get
a = 1, b = - 2, c = 3, d = 4
Thus, A = \(\left[\begin{array}{cc} 1 & -2 \\ 3 & 4 \end{array}\right]\)

(ii) A\(\left[\begin{array}{lll} 1 & 2 & 3 \\ 4 & 5 & 6 \end{array}\right]=\left[\begin{array}{rrr} -7 & -8 & -9 \\ 2 & 4 & 6 \end{array}\right]\)
Answer:
It is given that:
\(\mathrm{A}\left[\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \end{array}\right]=\left[\begin{array}{ccc} -7 & -8 & -9 \\ 2 & 4 & 6 \end{array}\right]\)
The matrix given on the R.H.S. of the equation is a 2 × 3 matrix and the one given on the L.H.S. of the equation is a 2 × 3 matrix.
Therefore, A is a 2 × 2 matrix.
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 10
Equating the corresponding elements of the two
matrices, we get
a + 4c = - 7
2a + 5c = 8 ........ (ii)
3a + 6c = - 9 ......... (iii)
b + 4d = 2 ....... (iv)
2b + 5d = 4 ........ (v)
3b + 6d = 6 ........ (vi)
Now, from (i), we have
a + 4c = - 7
⇒ a - 7 - 4c .......... (vii)
From (ii), we have
∴ 2a + 5c = - 8 ⇒ - 14 - 8c + 5c = - 8
⇒ - 3c = 6 ⇒ c = - 2
Substituting c = - 2 in Eq. (vii), we get
∴ a = - 7 - 4(- 2)
= - 7 + 8 = 1
Now, from (iv), we get
b + 4d = 2
⇒ b = 2 - 4d ...... (viii)
From eqs. (y) and (viii), we get
⇒ 4 - 8d + 5d = 4
⇒ - 3d = 0
⇒ d = 0
Substituting d = 0 in Eq. (viii), we get
∴ b = 2 - 4(0) = 2
Thus, a = 1, b = 2, c = - 2, d = 0
Hence, the required matrix A is \(\left[\begin{array}{cc} 1 & -2 \\ 2 & 0 \end{array}\right]\).

RBSE Class 12 Maths Important Questions Chapter 3 Matrices

Question 13.
If A = \(\left[\begin{array}{rr} -3 & 2 \\ 1 & -1 \end{array}\right]\) and I = \(\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]\), find scalar K so that A2 + I = KA.
Answer:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 11
On equating the corresponding elements, we get
- 3k = 12 ⇒ k = - 4

Question 14.
If A = \(\left[\begin{array}{c} -1 \\ 2 \\ 3 \end{array}\right] \)and B = [- 2 - 1 - 4], verify that (AB)T = BTAT.
Answer:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 12
From (i) and (ii), we get
(AB)T = BTAT
Hence, proved

RBSE Class 12 Maths Important Questions Chapter 3 Matrices

Question 15.
Show that the elements on the main diagonal of a skew symmetric matrix are all zero.
Answer:
Let A = [aij] be a skew-symmetric matrix.
Then aij = - aij for all i, j
Put i = j, we get
aii = - aii for all values of i
2aii = 0
= aii = 0 for all values of i
a11 = a22 = a33 = ........................ = am = 0
Thus, all the diagonals of a skew-symmetric matrix are zero.
Hence proved

Question 16.
If A = \(\left[\begin{array}{ll} 2 & 3 \\ 4 & 5 \end{array}\right]\), prove that A - AT, is a skew-symmetric matrix.
Answer:
Given, A = \(\left[\begin{array}{ll} 2 & 3 \\ 4 & 5 \end{array}\right]\)
Let B = A - AT
B is a skew -symmetric matrix if BT = - B
Now, B = A - AT
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 13

Question 17.
Express the matrix A = \(\left[\begin{array}{ccc} 4 & 2 & -1 \\ 3 & 5 & 7 \\ 1 & -2 & 1 \end{array}\right]\) as the sum of a symmetric and skew-symmetric matrix.
Answer:
Any square matrix A can be expressed as the sum of a symmetric and skew-symmetric, i.e., A = \(\frac{\mathrm{A}+\mathrm{A}^{\prime}}{2}\) + \(\frac{\mathrm{A}-\mathrm{A}^{\prime}}{2}\), where \(\frac{\mathrm{A}+\mathrm{A}^{\prime}}{2}\) and \(\frac{\mathrm{A}-\mathrm{A}^{\prime}}{2}\) are symmetric and skew-symmetric matrices respectively.
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 14
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 15
Thus, matrix A is expressed as the sum of symmetric matrix and skew-symmetric matrix.

RBSE Class 12 Maths Important Questions Chapter 3 Matrices

Question 18.
Express the matrix \(\left[\begin{array}{ccc} 3 & -2 & -4 \\ 3 & -2 & -5 \\ -1 & 1 & 2 \end{array}\right]\) as the sum of a symmetric and skew-symmetric matrix and verify your result.
Answer:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 16
Thus, matrix A is expressed as the sum of symmetric matrix and skew-symmetric matrix.

Question 19.
Find the matrix A = \(\left[\begin{array}{ll} 2 & 3 \\ 5 & 7 \end{array}\right]\), find A + AT and verify then it is a symmetric matrix.
Answer:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 17
Thus, (A + A)T is a symmetric matrix.
Hence proved.

Question 20.
Given a skew-symmetric matrix A = \(\left[\begin{array}{ccc} 0 & a & 1 \\ -1 & b & 1 \\ -1 & c & 0 \end{array}\right]\) the value of (a + b + c)2 is ................. .
Answer:
A = \(\left[\begin{array}{ccc} 0 & a & 1 \\ -1 & b & 1 \\ -1 & c & 0 \end{array}\right]\) is a skew-symmetric matrix, then the value of (a + b + c)2 is 0.

Question 21.
Express A = \(\left[\begin{array}{ll} 4 & -3 \\ 2 & -1 \end{array}\right]\) as a sum of a symmetric and a skew-symmetric matrix.
Answer:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 18
Thus, matrix A is expressed as the sum of symmetric matrix and skew-symmetric matrix.

RBSE Class 12 Maths Important Questions Chapter 3 Matrices

Question 22.
Show that the matrix A = \(\left[\begin{array}{lll} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{array}\right]\) satisfies the equation A2 - 4A - 5I3 = 0 and hence find A-1.
Answer:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 19
Now, A2 - 4A - 5I = 0
A2 - 4A = 5I
A2A- 1 - 4A.A-1 = 5IA-1
A - 4I = 5A-1
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 20

Question 23.
Find A-1, by using elementary row transformation for matrix A = \(\left[\begin{array}{ll} 3 & 2 \\ 7 & 5 \end{array}\right]\).
Answer:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 21

RBSE Class 12 Maths Important Questions Chapter 3 Matrices

Question 24.
Find the inverse of matrix A = \(\left[\begin{array}{ccc} 1 & 2 & -2 \\ -1 & 3 & 0 \\ 0 & -2 & 1 \end{array}\right]\) by using elementary row transformations.
Answer:
We know that
AA-1 = I
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 22

Question 25.
Find the inverse of each of the following matrices by using elementary row transformation.
(i) \(\left[\begin{array}{rr} 1 & 2 \\ 2 & -1 \end{array}\right]\)
Answer:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 23

(ii)
\(\left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right]\)
Answer:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 24

RBSE Class 12 Maths Important Questions Chapter 3 Matrices

(iii)
\(\left[\begin{array}{ccc} 2 & -1 & 4 \\ 4 & 0 & 2 \\ 3 & -2 & 7 \end{array}\right]\)
Answer:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 25
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 26

(iv) \(\left[\begin{array}{ccc} 3 & 0 & -1 \\ 2 & 3 & 0 \\ 0 & 4 & 1 \end{array}\right]\)
Answer:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 27

Question 26.
Obtain the inverse of the following matrix using elementary operations:
A = \(\left[\begin{array}{ccc} 2 & 1 & -3 \\ -1 & -1 & 4 \\ 3 & 0 & 2 \end{array}\right]\)
Answer:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 28

RBSE Class 12 Maths Important Questions Chapter 3 Matrices

Question 27.
If A = \(\left[\begin{array}{rrr} 1 & 3 & 2 \\ 2 & 0 & -1 \\ 1 & 2 & 3 \end{array}\right]\), then show that A3 - 4A2 - 3A +111 = 0. Hence, find A-1.
Answer:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 29
Now, A3 - 4A2 - 3A + 111 = 0
Pre-multiplied by A-1, we get
A-1A3 - 4A-1A2 - 3A-1A + 11A-1
⇒ A2 - 4A - 3I + 11A-1 = 0 [∵ A-1A = I]
⇒ 11A-1 = 3I + 4A - A2
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 30

Multiple Choice Questions

Question 1.
If A = [2, -3, 4], B = \(\left[\begin{array}{l} 3 \\ 2 \\ 2 \end{array}\right]\), X = [1, 2, 3] and Y = \(\left[\begin{array}{l} 2 \\ 3 \\ 4 \end{array}\right]\), then AB + XY equals:
(a) [28]
(b) [24]
(c) 28
(d) 24
Answer:
(a) [28]

Question 2.
If A = \(\left[\begin{array}{lll} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{array}\right]\), A-1 = \(\left[\begin{array}{rrr} \frac{1}{2} & -\frac{1}{2} & \frac{1}{2} \\ -4 & 3 & c \\ \frac{5}{2} & -\frac{3}{2} & \frac{1}{2} \end{array}\right]\), then:
(a) a = 2, c = -\(\frac{1}{2}\)
(b) a = 1, c = -1
(c) a = -1, c = 1
(d) a = \(\frac{1}{2}\), c = \(\frac{1}{2}\)
Answer:
(b) a = 1, c = -1

RBSE Class 12 Maths Important Questions Chapter 3 Matrices 

Question 3.
If A = \(\left[\begin{array}{rrr} 1 & 2 & 1 \\ 5 & 2 & 6 \\ -2 & -1 & -3 \end{array}\right]\), then A3 = ________________
(a) I
(b) AT
(c) O
(d) A-1
Answer:
(c) O

Question 4.
If A = \(\left[\begin{array}{rr} 3 & -4 \\ 1 & -1 \end{array}\right]\), then An = ________________
(a) \(\left[\begin{array}{cc} 3 n & -4 n \\ n & -n \end{array}\right]\)
(b) \(\left[\begin{array}{rr} 2+n & 5-n \\ n & -n \end{array}\right]\)
(c) \(\left[\begin{array}{ll} 3^n & (-4)^n \\ 1^n & (-1)^n \end{array}\right]\)
(d) \(\left[\begin{array}{rc} 2 n+1 & -4^n \\ n & -1-2 n \end{array}\right]\)
Answer:
(d) \(\left[\begin{array}{rc} 2 n+1 & -4^n \\ n & -1-2 n \end{array}\right]\)

Question 5.
Suppose a matrix A satisfies A2 - 5A + 7I = O. If A5 = aA + bI then the value of 2a - 3b must be ....
(a) 4135
(b) 1435
(c) 1453
(d) 3145
Answer:
(c) 1453

Question 6.
If A = \(\left[\begin{array}{lll} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right]\), then A2013 = ............
(a) 32013A
(b) -32012I
(c) 32011A
(d) 31006A
Answer:
(c) 32011A

Question 7.
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 1
Provided θ - Φ = ......, n ∈ Z
(a) nπ
(b) \(\frac{(2 n+1) \pi}{2}\)
(c) \(\frac{n \pi}{2}\)
(d) 2nπ
Answer:
(b) \(\frac{(2 n+1) \pi}{2}\)

Question 8.
If A = \(\left[\begin{array}{ll} \alpha & 0 \\ 1 & 1 \end{array}\right]\) and B = \(\left[\begin{array}{ll} 1 & 0 \\ 5 & 1 \end{array}\right]\), then A2 = B for
(a) α = 4
(b) α = 1
(c) α = -1
(d) no α
Answer:
(d) no α

Question 9.
If A = \(\left[\begin{array}{ll} \alpha & 0 \\ 2 & 3 \end{array}\right]\) and I = \(\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]\), then A2 = 9I for
(a) α = 4
(b) α = 3
(c) α = -3
(d) no α =
Answer:
(c) α = -3

Question 10.
If A = \(\left[\begin{array}{rr} 3 & 1 \\ -9 & -3 \end{array}\right]\), then I + 2A + 3A2 + ........ + ∞ = ...........
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 2
Answer:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 3

RBSE Class 12 Maths Important Questions Chapter 3 Matrices

Question 11.
If A = \(\left[\begin{array}{rr} 1 & 0 \\ -1 & 7 \end{array}\right]\) and A2 = 8A + kI2, then k = ...........
(a) 1
(b) -1
(c) 7
(d) -7
Answer:
(d) -7

Question 12.
The identity element in the group M = {\(\left[\begin{array}{lll} x & x & x \\ x & x & x \\ x & x & x \end{array}\right]\)/ x ∈ R, x ≠ 0} with respect to matrix multiplication is ............
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 4
Answer:
RBSE Class 12 Maths Important Questions Chapter 3 Matrices 5

Fill in the blanks:

Question 1.
If A + B = \(\left[\begin{array}{ll} 1 & 0 \\ 1 & 1 \end{array}\right]\) and A - 2B =\(\left[\begin{array}{cc} -1 & 0 \\ 1 & -1 \end{array}\right]\), then A = ________________
Answer:
\(\left[\begin{array}{ll} \frac{1}{3} & \frac{1}{3} \\ \frac{2}{3} & \frac{1}{3} \end{array}\right]\)

Question 2.
If \(\left[\begin{array}{cc} x+y & 7 \\ 9 & x-y \end{array}\right]=\left[\begin{array}{cc} 2 & 7 \\ 9 & 4 \end{array}\right]\), then x,y ________________
Answer:
-3

Question 3.
If [2 1 3] \(\left[\begin{array}{ccc} -1 & 0 & -1 \\ -1 & 1 & 0 \\ 0 & 1 & 1 \end{array}\right]\left[\begin{array}{c} 1 \\ 0 \\ -1 \end{array}\right]\) = A, then the order of matrix A is ________________
Answer:
1 × 1

Question 4.
If matrix A = \(\left[\begin{array}{cc} 1 & -1 \\ -1 & 1 \end{array}\right]\) and A2 = KA, then the value of k is ________________
Answer:
2

RBSE Class 12 Maths Important Questions Chapter 3 Matrices

Question 5.
If \(\left[\begin{array}{ll} 1 & 3 \\ 4 & 5 \end{array}\right]\left[\begin{array}{l} x \\ 2 \end{array}\right]=\left[\begin{array}{l} 5 \\ 6 \end{array}\right]\), then x = ________________
Answer:
-1

True/False

Question 1.
In the matrix, the number or function is called the data of the matrix.
Answer:
False

Question 2.
A matrix having m rows and n columns is called a matrix of order n*m.
Answer:
False

Question 3.
A matrix is said to be a column matrix if it has only one column.
Answer:
True

Question 4.
A matrix is said to be diagonal matrix if all its elements are zero.
Answer:
False

Question 5.
Two matrices are said to be equal if they are of the same order.
Answer:
True

Prasanna
Last Updated on Nov. 13, 2023, 9:58 a.m.
Published Nov. 12, 2023