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

If `[(x + 2, 7),(y + 3, a - 2)] = [(4, b - 3),(4, 3)]`, the value of x, y, a and b are ______.

If A = `[(5, -5),(3, -3)]` and B = `[(-5, 5),(-3, 3)]`; the value of matrix (A – B) is ______.

If A = `[(5, 5),(4, 0)]`, B = `[(3, 2),(1, 4)]` and C = `[(-2, 3),(2, 1)]` then matrix (A + B – C) is ______.

If A = `[(7, 5),(-3, 3)]` and B = `[(-2, 5),(1, 0)]`, then the matrix P (such that A + P = B) is ______.

The additive inverse of matrix A + B, where A = `[(4, 2),(7, -2)]` and B = `[(-2, 1),(3, -4)]` is ______.

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.

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)]`

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

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

If `4[(5, x)] - 5[(y, -2)] = [(10, 22)]`, the values of x and y are ______.

If A = `[(-3, -7),(0, -8)]` and A – B = `[(6, 4),(-3, 0)]`, then matrix B is ______.

If I is a unit matrix of order 2 and M + 4I = `[(8, -3),(4, 2)]`, the matrix M is ______.

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

Given A = `[(4, 7),(3, -2)]` and B = `[(1, 2),(-1, 4)]`, then A – 2B is ______.

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

If A is a matrix of order m × 3, B is a matrix of order 3 × 2 and R is a matrix of order 5 × n such that AB = R, the value of m and n are ______.

If A = `[(4, x),(0, 1)]`, B = `[(2, 12),(0, 1)]` and A = B², the value of x is ______.

 A, B and C are three square matrices each of order 3; the order of matrix CA + B² is ______.

If A = `[(5, -2),(7, 0)]` and B = `[(8),(3)]`, then which of the following is not possible?

If A = `[(1, 0),(1, 1)]`, B = `[(0, 1),(1, 0)]` and C = `[(1, 1),(0, 0)]`, the matrix A² + 2B – 3C is ______.

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

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?

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.

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

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

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:

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

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

If a matrix A = `[(0, 1),(2, -1)]` and matrix B = `[(3),(1)]`, then which of the following is possible:

If `M xx [(3, 2),(-1, 0)] = [(3, -1)]`, the order of matrix M is ______.

If `[(2x - y),(x + y)] = [(9),(9)]`, the value of x and y are ______.

If matrix A = `[(x - y, x + y),(y - x, y + x)]` and matrix B = `[(x + y, y - x),(x - y, y + x)]` then A + B is ______.

Event A: Order of matrix A is 3 × 5.

Event B: Order of matrix B is 5 × 3.

Event C: Order of matrix C is 3 × 3.

Product of which two matrices gives a square matrix.

Two matrices \[A\] and \[B\] each of order \[2 \times 2.\]

Assertion (A): \[A \times B = 0 \nRightarrow A = 0\] or \[B = 0.\]

Reason (R): Let \[A = \begin{bmatrix} 2 & 2 \\ 5 & 5 \end{bmatrix} \neq 0\] and \[B = \begin{bmatrix} -4 & 3 \\ 4 & -3 \end{bmatrix} \neq 0\]

but \[A \times B = \begin{bmatrix} 2 & 2 \\ 5 & 5 \end{bmatrix} \begin{bmatrix} -4 & 3 \\ 4 & -3 \end{bmatrix} = 0\]

Matrix \[A = \begin{bmatrix} x & y \end{bmatrix}\] and Matrix \[B = \begin{bmatrix} a \\ b \end{bmatrix}.\]

Assertion (A): Product BA is possible and order of resulting matrix is \[2 \times 2.\]

Reason (R): The product BA of two matrices A and B is possible only if number of rows in matrix B is same as number of columns in matrix A.

A, B and C are three matrices each of order 2 × 2.

Statement (1): If A × B = A × C ⇒ B = C.

Statement (2): Cancellation law is applicable in matrix multiplication.

Matrix A =\[\begin{bmatrix} 2 & -2 \\ -2 & 2 \end{bmatrix}\] and matrix B = \[ \begin{bmatrix} 5 & 5 \\ 5 & 5 \end{bmatrix}\]

Statement (1): AB = 0.

Statement (2): AB = 0, even if A ≠ 0 and B ≠ 0

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)

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.

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’.

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

Let A = `[(1, 0),(2, 1)]`, B = `[(2, 3),(-1, 0)]`, Find A² + AB + B².

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.

Evaluate:

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

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

Given matrix A `[(4 sin 30°, cos 0°),(cos 0°, 4 sin 30°)]` and B = `[(4),(5)]`. If AX = B.

1. Write the order of matrix X.
2. Find the matrix ‘X’.

Neeta, Salma and Vivian are neighbours in different flats of the same building. Last Sunday, they went together to a departmental store to buy groceries.
The groceries purchased by them is as shown below.

The prices of the items are as follows:

Pulses: ₹ 170 per kg
Tea: ₹ 150 per packet
Refined oil: ₹ 250 per litre

Using matrix multiplication, find the total amount that Neeta, Salma and Vivian paid.