Selina solutions for Mathematics [English] Class 10 ICSE chapter 9 - Matrices [Latest edition]

State, whether the following statement is true or false. If false, give a reason.

If A and B are two matrices of orders 3 × 2 and 2 × 3 respectively; then their sum A + B is possible.

State, whether the following statement is true or false. If false, give a reason.

The matrices A_2 × 3 and B_2 × 3 are conformable for subtraction.

State, whether the following statement is true or false. If false, give a reason.

Transpose of a 2 × 1 matrix is a 2 × 1 matrix.

State, whether the following statement is true or false. If false, give a reason.

Transpose of a square matrix is a square matrix.

State, whether the following statement is true or false. If false, give a reason.

A column matrix has many columns and only one row.

Given : `[(x, y + 2),(3, z - 1)] = [(3, 1),(3, 2)]`; find x, y and z.

Solve for a, b and c; if `[(-4, a + 5),(3, 2)] = [(b + 4, 2),(3, c- 1)]`

Solve for a, b and c; if `[(a, a - b),(b + c, 0)] = [(3, -1),(2, 0)]`

If A = `[(8, -3)]` and B = `[(4, -5)]`; find A + B

If A = `[(8, -3)]` and B = `[(4, -5)]`; find B – A

If `A = [(2),(5)], B = [(1),(4)]` and `C = [(6),(-2)]`, find B + C

If `A = [(2),(5)], B = [(1),(4)]` and `C = [(6),(-2)]`, find A – C

If `A = [(2),(5)], B = [(1),(4)]` and `C = [(6),(-2)]`, find A + B – C

If `A = [(2),(5)], B = [(1),(4)]` and `C = [(6),(-2)]`, find A – B + C

Wherever possible, write the following as a single matrix.

`[(1, 2),(3, 4)] + [(-1, -2),(1, -7)]`

Wherever possible, write the following as a single matrix.

`[(2, 3, 4),(5, 6, 7)] - [(0, 2, 3),(6, -1, 0)]`

Wherever possible, write the following as a single matrix.

`[(0, 1, 2),(4, 6, 7)] + [(3, 4),(6, 8)]`

Find x and y from the given equations:

`[(5, 2),(-1, y - 1)] - [(1, x - 1),(2, -3)] = [(4, 7),(-3, 2)]`

Find x and y from the given equations:

`[(-8, x)] + [(y, -2)] = [(-3, 2)]`

Given : M = `[(5, -3),(-2, 4)]`, find its transpose matrix M^t. If possible, find M + M^t

Given : M = `[(5, -3),(-2, 4)]`, find its transpose matrix M^t. If possible, find M^t – M

Write the additive inverse of matrices A, B and C:

Where `A = [(6, -5)]; B = [(-2, 0),(4, -1)]` and `C = [(-7), (4)]`.

Given `A = [(2, -3)], B = [(0, 2)]` and `C = [(-1, 4)]`; find the matrix X in the following:

X + B = C – A

Given `A = [(2, -3)], B = [(0, 2)]` and `C = [(-1, 4)]`; find the matrix X in the following:

A – X = B + C

Given `A = [(-1, 0),(2, -4)]` and `B = [(3, -3),(-2, 0)]`; find the matrix X in the following:

A + X = B

Given `A = [(-1, 0),(2,-4)]` and `B = [(3, -3),(-2, 0)]`; find the matrix X in the following:

A – X = B

Given `A = [(-1, 0),(2, -4)]` and `B = [(3, -3),(-2, 0)]`; find the matrix X in the following:

X – B = A

Evaluate:

`3[(5, -2)]`

Evaluate:

`7[(-1, 2),(0, 1)]`

Evaluate:     

`2[(-1      0)/(2 -3)]  +[(3      3)/(5    0)]`

Evaluate:

`6[(3),(-2)] -2[(-8),(1)]`

Find x and y if `3[(4,  x)] + 2[(y, -3)] = [(10, 0)]`

Find x and y if `x[(-1), (2)] - 4[(-2), (y)] = [(7),(-8)]`

Given `A = [(2, 1),(3, 0)], B = [(1, 1),(5, 2)]` and `C = [(-3, -1),(0, 0)]`; find 2A – 3B + C

Given `A = [(2, 1),(3, 0)], B = [(1, 1),(5, 2)]` and `C = [(-3, -1),(0, 0)]`; find A + 2C – B

If `[(4, -2),(4, 0)] + 3A = [(-2, -2),(1, -3)]`; find A.

Given `A = [(1, 4),(2, 3)] and B = |(-4-1),(-3 -2)|`

Find the matrix 2A  + B

Given `A = [(1   4),(2  3)] and B = [(-4 -1),(-3 -2)]` Find the matrix C such that C + B = `[(0, 0),(0,0)]`

If `2[(3, x),(0, 1)] + 3[(1, 3),(y, 2)] = [(z, -7),(15, 8)]`; find the values of x, y and z.

Given A = `[(-3, 6),(0, -9)]` and A^t is its transpose matrix. Find 2A + 3A^t 

Given A = `[(-3, 6),(0, -9)]` and A^t is its transpose matrix. Find 2A^t – 3A

Given A = `[(-3, 6),(0, -9)]` and A^t is its transpose matrix. Find `1/2 A - 1/3 A^t`

Given A = `[(-3, 6),(0, -9)]` and A^t is its transpose matrix. Find `A^t - 1/3 A`

Given `A = [(1, 1),(-2, 0)]` and `B = [(2, -1),(1, 1)]`. Solve for matrix X:

X + 2A = B

Given `A = [(1, 1),(-2, 0)]` and `B = [(2, -1), (1, 1)]`. Solve for matrix X:

3X + B + 2A = 0

Given `A = [(1, 1),(-2, 0)]` and `B = [(2, -1),(1, 1)]`. Solve for matrix X:

3A – 2X = X – 2B

If `M = [(0), (1)]` and `N = [(1),(0)]`, show that `3M + 5N = [(5),(3)]`

If I is the unit matrix of order 2 × 2; find the matrix M, such that `M - 2I = 3[(-1, 0),(4, 1)]`

If I is the unit matrix of order 2 × 2; find the matrix M, such that `5M + 3I = 4[(2, -5),(0, -3)]`

If `[(1, 4),(-2, 3)] + 2M = 3[(3, 2),(0, -3)]`, find the matrix M 

Evaluate if possible `[(3, 2)][(2),(0)]`

Evaluate if possible `[(1, -2)][(-2, 3),(-1, 4)]`

Evaluate if possible `[(6, 4),(3, -1)][(-1),(3)]`

Evaluate if possible `[(6, 4),(3, -1)][(-1, 3)]`

If A = `[(0, 2),(5, -2)]`, B = `[(1, -1),(3, 2)]` and I is a unit matrix of order 2 × 2, find AB

If A = `[(0, 2),(5, -2)]`, B = `[(1, -1),(3, 2)]` and I is a unit matrix of order 2 × 2, find BA

If A = `[(0, 2),(5, -2)]`, B =` [(1, -1),(3, 2)]` and I is a unit matrix of order 2 × 2, find AI

If A = `[(0, 2),(5, -2)]`, B = `[(1, -1),(3, 2)]` and I is a unit matrix of order 2 × 2, find IB

If A = `[(0, 2),(5, -2)]`, B = `[(1, -1),(3, 2)]` and I is a unit matrix of order 2 × 2, find A²

If A = `[(0, 2),(5, -2)]`, B = `[(1, -1),(3, 2)]` and I is a unit matrix of order 2 × 2, find B²A

If A = `[(3, x),(0, 1)]` and B = `[(9, 16),(0, -y)]`, find x and y when A² = B.

Find x and y, if `[(4, 3x),(x, -2)][(5), (1)] = [(y),(8)]`

Find x and y, if `[(x, 0),(-3, 1)][(1, 1),(0, y)] = [(2, 2),(-3, -2)]`

If A = `[(1, 3),(2, 4)]`, B = `[(1, 2),(4, 3)]` and C = `[(4, 3),(1, 2)]`, find:

1. (AB)C
2. A(BC)

Is A(BC) = (AB)C?

Given A = `[(0, 4, 6),(3, 0, -1)]` and B = `[(0, 1),(-1, 2),(-5, -6)]`, find if possible AB

Given A = `[(0, 4, 6),(3, 0, -1)]` and B = `[(0, 1),(-1, 2),(-5, -6)]`, find if possible BA

Given A = `[(0, 4, 6),(3, 0, -1)]` and B = `[(0, 1),(-1, 2),(-5, -6)]`, find if possible A²

Let A = `[(2, 1),(0, -2)]`, B = `[(4, 1),(-3, -2)]` and C = `[(-3, 2),(-1, 4)]`. Find A² + AC – 5B.

If M = `[(1, 2),(2, 1)]` and I is a unit matrix of the same order as that of M; show that: M² = 2M + 3I.

If A = `[(a, 0),(0, 2)]`, B = `[(0, -b),(1, 0)]`, M = `[(1, -1),(1, 1)]` and BA = M², find the values of a and b.

Given A = `[(4, 1),(2,3)]` and B = `[(1, 0),(-2, 1)]`, find A – B

Given A = `[(4, 1),(2, 3)]` and B = `[(1, 0),(-2, 1)]`, find A²

Given A = `[(4, 1),(2, 3)]` and B = `[(1, 0),(-2, 1)]`, find AB.

Given A = `[(4, 1),(2, 3)]` and B = `[(1, 0),(-2, 1)]`, find A² – AB + 2B

If A = `[(1, 4), (1, -3)]` and B = `[(1, 2),(-1, -1)]`, find:

1. (A + B)²
2. A² + B²
3. Is (A + B)² = A² + B² ?

Find the matrix A, If B =`[(2,1),(0,1)] and B^2 = B+1/2A`

If A = `[(-1, 1),(a, b)]` and A² = I, find a and b.

If A = `[(2, 1),(0, 0)]`, B = `[(2, 3),(4, 1)]` and C = `[(1, 4),(0, 2)]`; then show that A(B + C) = AB + AC.

If A = `[(2, 1),(0, 0)]`, B = `[(2, 3),(4, 1)]` and C = `[(1, 4),(0, 2)]`; then show that (B – A)C = BC – AC.

If A = `[(1, 4),(2, 1)]`, B = `[(-3, 2),(4, 0)]` and C = `[(1, 0),(0, 2)]`, simplify : A² + BC.

Solve for x and y:

`[(2, 5),(5, 2)][(x),(y)] = [(-7),(14)]`

Solve for x and y:

`[(x + y, x - 4)][(-1, -2),(2, 2)] = [(-7, -11)]`

Solve for x and y `[(-2,0), (3,1)][(-1), (2x)] +3[(-2), (1)] =2[(y), (3)]`

In the given case below find

a) The order of matrix M.

b) The matrix M

`M xx [(1,1),(0, 2)] = [1, 2]`

In the given case below, find:

1. the order of matrix M.
2. the matrix M.

1. `M xx [(1, 1),(0, 2)] = [(1, 2)]`
2. `[(1, 4),(2, 1)] xx M = [(13), (5)]`

If A = `[(2, x),(0, 1)]` and B = `[(4, 36),(0, 1)]`; find the value of x, given that A² = B.

If A = `[(3, 7),(2, 4)]`, B = `[(0, 2),(5, 3)]` and C = `[(1, -5),(-4, 6)]`. Find AB – 5C.

If A and B are any two 2 × 2 matrices such that AB = BA = B and B is not a zero matrix, what can you say about the matrix A?

Given A = `[(3, 0),(0, 4)]`, B = `[(a, b),(0, c)]` and that AB = A + B; find the values of a, b and c.

If P = `[(1, 2),(2, -1)]` and Q = `[(1, 0),(2, 1)]`, then compute:

1. P² – Q²
2. (P + Q)(P – Q)

Is (P + Q)(P – Q) = P² – Q² true for matrix algebra?

Given the matrices:

A = `[(2, 1),(4, 2)]`, B = `[(3, 4),(-1, -2)]` and C = `[(-3, 1),(0, -2)]`. Find: 

1. ABC
2. ACB.
   State whether ABC = ACB.

If A = `[(1, 2),(3, 4)]`, B = `[(6, 1), (1, 1)]` and C = `[(-2, -3),(0, 1)]`, find the following and state if they are equal CA + B

If A = `[(1, 2),(3, 4)]`, B = `[(6, 1),(1, 1)]` and C = `[(-2, -3),(0, 1)]`, find the following and state if they are equal A + CB

If A = `[(2, 1),(1, 3)]` and B = `[(3),(-11)]`, find the matrix X such that AX = B.

If A = `[(4, 2),(1,1)]`, find (A – 2I)(A – 3I).

If A = `[(2, 1, -1),(0, 1, -2)]`, Find A^t . A where A^t is the transpose of matrix A.

If A = `[(2, 1, -1),(0, 1, -2)]`, Find A . A^t where A^t is the transpose of matrix A.

If M = `[(4,1),(-1,2)]`, show that 6M – M² = 9I; where I is a 2 × 2 unit matrix.

If `P = [(2,6),(3,9)]` and `Q = [(3,x),(y, 2)]` find x and y such that PQ = null matrix

Evaluate without using tables:

`[(2cos 60°, -2sin 30°),(-tan45°, cos 0°)] [(cos 45°, cosec  30°),(sec 60°, sin 90°)]`

State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.

A + B = B + A

State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.

A – B = B – A

State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.

(B . C) . A = B . (C . A)

State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.

 (A + B) . C = A . C + B . C

State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.

A . (B – C) = A . B – A . C

State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.

(A – B) . C = A . C – B . C

State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.

A² – B² = (A + B) (A – B)

State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.

(A – B)² = A² – 2A . B + B²

Find x and y, if `[(3, -2),(-1, 4)][(2x),(1)] + 2[(-4),(5)] = 4[(2),(y)]`

Find x and y, if `[(3x, 8)][(1, 4),(3, 7)] - 3[(2, -7)] = 5[(3, 2y)]`

If `[(x, y)][(x),(y)] = [25]` and `[(-x, y)][(2x),(y)] = [-2]`; find x and y, if:

1. x, y ∈ W (whole numbers)
2. x, y ∈ Z (integers)

If `[x, y][(x),(y)] = [25]` and `[(-x, y)][(2x),(y)] = [-2]` find x and y if `x, y ∈  Z` (integer)

Given `[(2, 1),(-3, 4)] X = [(7), (6)]` write the order of matrix x

Given `[(2, 1),(-3, 4)] x = [(7),(6)]` Write the matrix x.

Evaluate:

`[(cos 45°, sin 30°),(sqrt(2) cos 0°, sin 0°)] [(sin 45°, cos 90°),(sin 90°, cot 45°)]`

If A = `[(0, -1),(4, -3)]`, B = `[(-5),(6)]` and 3A × M = 2B; find matrix M.

If `[(a, 3),(4, 1)] + [(2, b),(1, -2)] - [(1, 1),(-2, c)] = [(5, 0),(7, 3)]`, find the values of a, b and c.

If A = `[(1, 2),(2, 1)]` and B = `[(2, 1),(1, 2)]`; find A(BA)

If A = `[(1, 2),(2, 1)]` and B = `[(2, 1),(1, 2)]`; find (AB)B

Find x and y, if : `[(x, 3x),(y, 4y)][(2),(1)] = [(5),(12)]`.

If matrix X = `[(-3, 4),(2, -3)][(2),(-2)]` and 2X – 3Y = `[(10),(-8)]`, find the matrix ‘X’ and matrix ‘Y’.

Given A = `[(2, -1),(2, 0)]`, B = `[(-3, 2),(4, 0)]` and C = `[(1, 0),(0, 2)]`, find the matrix X such that : A + X = 2B + C.

Find the value of x, given that A² = B,

A = `[(2, 12),(0, 1)]` and B = `[(4, x),(0, 1)]`

If `A = [(2, 5),(1, 3)]`, `B = [(4, -2),(-1, 3)]` and I is Identity matrix of same order and `A^t` is the transpose of matrix A find `A^t.B + BI`

Given A = `[(2, -6),(2, 0)]`, B = `[(-3, 2),(4, 0)]` and C = `[(4, 0),(0, 2)]`. Find the matrix X such that A + 2X = 2B + C.

Let A = `[(4, -2),(6, -3)]`, B = `[(0, 2),(1, -1)]` and C = `[(-2, 3),(1, -1)]`. Find A² – A + BC

Let `A = [(1, 0),(2, 1)], B = [(2, 3),(-1, 0)]`. Find `A^2 + AB + B^2`

If A = `[(3, a),(-4, 8)]`, B = `[(c, 4),(-3, 0)]`, C = `[(-1, 4),(3, b)]` and 3A – 2C = 6B, find the values of a, b and c.

Given A = `[(p, 0),(0, 2)]`, B = `[(0, -q),(1, 0)]`, C = `[(2, -2),(2, 2)]` and BA = C². Find the values of p and q.

Given A = `[(3, -2),(-1, 4)]`, B = `[(6),(1)]`, C = `[(-4),(5)]` and D = `[(2),(2)].` Find : AB + 2C – 4D

Evaluate:

`[(4 sin 30°, 2 cos 60°),(sin 90°, 2 cos 0°)] [(4, 5),(5, 4)]`

If A = `[(3, 1),(-1, 2)]` and I = `[(1, 0),(0, 1)]`, find A² – 5A + 7I.

Given A = `[(2,0), (-1,7)] and 1 = [(1,0), (0,1)]` and A² = 9A +mI. Find m

Given matrix A = `[(4sin30^@,cos0^@), (cos0^@,4sin30^@)] and B = [(4), (5)]` If AX = B.
Write the order of matrix X.

Given matrix A = `[(4sin30^@,cos0^@), (cos0^@,4sin30^@)] and B = [(4), (5)]` If AX = B.
 Find the matrix 'X'

If A = `[(1,3), (3,4)]` B = `[(-2,1), (-3,2)]` and `A^2 - 5B^2 = 5C` Find the matrix C where C is a 2 by 2 matrix. 

Given matrix B =`[(1,1), (8,3)]` Find the matrix X if, X = B² - 4B. Hence, solve for a and b given X`[(a), (b)] = [(5), (50)]`