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# Selina solutions for Class 10 Mathematics chapter 9 - Matrices

## Chapter 9 : Matrices

#### Page 0

State, whether the following statements are 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 statements are true or false. If false, give a reason.

The matrices A2 × 3 and B2 × 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 statements are true or false. If false, give a reason.

Transpose of a square matrix is a square matrix.

State, whether the following statements are true or false. If false, give a reason.

A column matrix has many columns and one row.

Given [(x, y + 2),(3, z - 1)] = [(3,1),(3,2)], Find x, y, 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 of the following as a single matrix

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

Wherever possible write of the following as a single matrix

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

Wherever possible write of 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 matrx 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),(2,0)] and B = [(3, -3),(-2, 0)] find the matrix X in of the following

A- X = B

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

X - B = A

#### Page 0

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[(2, 1),(3, 0)],-3[(1, 1),(5, 2)] + [(-3, -1),(0,0)] Find 2A - 3B + C

Given A =  2[(2,1),(3,0)]-3[(1,1),(5,2)]+[(-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 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 = O

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 x 2 Find the matrix M such that M - 2I = 3[(-1, 0),(4, 1)]

If I is the unit matrix of order 2 x 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

#### Page 0

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 x 2 find AB

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

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

If A= [(0, 2),(5, -2)], B = [(1, -1),(3, 2)] and I is unit matrix of order 2 x 2 Find IB

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

If A = [(0, 2),(5, -2)], B = [(1, -1),(3, 2)] and I is unit matrix of order 2 x 2 find B^2A

If M = [(2,1),(1,-2)] ; find M2, M3 and M5.

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)][(0, 1),(-1, 2),(-5, -6)] Find if possible A^2

If A = [(1, -2 ,1), (2,1,3)] and B= [(2,1),(3,2),(1,1)];

Write down the product matrix AB.

If A = [(1,-2 ,1),(2,1,3)]and B=[(2,1),(3,2),(1,1)]

would it be possible to form the product matrix BA? If so, compute BA; if not give a reason
why it is not possible.

If M =[(1, 2),(2, 1)] and I is a unit matrix of the same order as that of M Show that M^2 = 2M + 3I

If A = [(a, 0),(0, 2)], B = [(0, -b),(1, 0)], M = [(1, -1),(1, 1)] and BA = M^2 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 A^2

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 A^2 - AB + 2B

If A  = [(1, 4), (1, -3)] and B = [(1, 2),(-1, -1)] Find (A + B)^2

If A = [(1, 4),(1, -3)] and B = [(1, 2),(-1, -1)] Find A^2 + B^2

If A= [(1, 4), (1, -3)] and B = [(1, 2),(-1, -1)] Find :  Is (A + B)^2 = A^2 + B^2?

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

If A = [(-1, 1),(a, b)] and A^2 = 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 A^2 + BC

Solve for x and y: [(2, 5),(5, 2)][(x),(y)] = [(-7),(14)]

Solve for x and y :

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

Solve for x and y :

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

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 :

a) The order of matrix M

b) The matrix M

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

If A = [(2, x),(0, 1)] and B = [(4, 36),(0, 1)]. Find the vlaue of x given that A^2 = B

Find the positive integers p and q such that :

[p   q][p/q]= [25]

If A and B are any two 2 x 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) P^2 - Q^2

2) (P + Q)(P - Q)

Is (P + Q)(P - Q) = P^2 - Q^2 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 of they are equal CA + B

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

if A = [(2, 1),(1, 3)] and B = [(3),(-11)] Fidn 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.A 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 - m^2 = 9I where I is 2 x 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:

[(2 cos 60^@ - 2 sin 30^@),(-tan 45^@ , cos 0^@)][(cot 45^@,cosec 30^@),(sec 60^@,sin 90^@)]

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

A + B = B + A

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

A – B = B – A

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

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

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

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

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

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

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

(A – B). C = A. C – B. C

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

A² – B² = (A + B) (A – B)

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

(A – B)² = A² – 2A. B + B²

#### Page 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 x, y  ε  W (whole numbers)

If [x, y][(x),(y)] = [25] and [(-x, y)][(2x),(y)] = [-2] find x and y if x, y  ε  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°),(sqrt2 cos 0°, sin 0°)][(sin 45°, cos 90°), (sin 90°, cot 45°)]

If A = [(0, -1),(4, -3)], B = [(-5),(6)] and 3A x 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 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 A^2 = 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)], 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 A^2 + 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 , c.

Given A = [(p, 0),(0, 2)], B = [(0, -q),(1, 0)]  C = [(2, -2),(2, 2)] and BA = C^2 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:

[(4sin 30^@,  2cos 60^@),(sin 90^@, 2 cos 0^@)][(4,5),(5,4)]

if A = [(3,1),(-1,2)] and I = [(1,0),(0,1)], find A^2 - 5A + 7I

## Selina solutions for Class 10 Mathematics chapter 9 - Matrices

Selina solutions for Class 10 Maths chapter 9 (Matrices) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Selina ICSE Concise Mathematics for Class 10 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. Selina textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10 Mathematics chapter 9 Matrices are Introduction to Matrices, Addition and Subtraction of Matrices, Multiplication of Matrix, Matrices Examples.

Using Selina Class 10 solutions Matrices exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Selina Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 10 prefer Selina Textbook Solutions to score more in exam.

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