# Matrices Selina Concise Solutions Chapter 9 for ICSE Class 10

## Selina Publishers Solutions Chapter-9 Matrices

**Matrices Selina Concise Solutions** Chapter 9 for ICSE Class 10. Solutions of Exercise – 9 (A), Exercise – 9 (B), Exercise – 9 (C), Exercise – 9 (D), for** Concise **Selina Maths for ICSE Board Class 10th. **Concise Solutions Matrices **Chapter – 9 for ICSE Maths Class 10 is available here. All **Solutions **of **Concise** **Selina** of Chapter 9 **Matrices** has been solved according instruction given by council. This is the **Solutions **of Chapter-9 **Matrices** for ICSE Class 10th. ICSE Maths text book of **Concise** is In series of famous ICSE writer in maths. **Concise** is most famous among students.

**Matrices Selina Concise Solutions Chapter 9 for ICSE Class 10**

The Solutions of Concise Mathematics Chapter 9 **Matrices** for ICSE Class 10 have been solved. Experience teachers Solved Chapter-9 Matrices to help students of class 10th ICSE board. Therefore the ICSE Class 10th Maths Solutions of Concise Selina Publishers helpful on various topics which are prescribed in most ICSE Maths textbooks

**Select Topics of Chapter- 9 Matrices Selina Concise Solutions **

**How to Solve Concise Maths Selina Publications Chapter-9 Matrices**

Note:- Before viewing **Solutions** of **Chapter -9 Matrices **of **Concise Selina Maths **read the Chapter Carefully then solve all example of your text book**. The Chapter- 9 Matrices **is main Chapter in ICSE board** .**

**Exercise – 9 (A) , of Chapter-9 Matrices for Concise Solutions for ICSE Class 10th Mathematics ( Selina Publishers)**

#### Question 1

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

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

(ii) The matrices and are conformable for subtraction.

(iii) Transpose of a 2 1 matrix is a 2 1 matrix.

(iv) Transpose of a square matrix is a square matrix.

(v) A column matrix has many columns and one row.

#### Answer 1

(i) False

The sum A + B is possible when the order of both the matrices A and B are same.

(ii) True

(iii) False

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

(iv) True

(v) False

A column matrix has only one column and many rows.

#### Question 2

Given: ,………… find x, y and z.

#### Answer 2

If two matrices are equal, then their corresponding elements are also equal. Therefore, we have:

x = 3,

y + 2 = 1 y = -1

z – 1 = 2 z = 3

#### Question 3

Solve for a, b and c if………….

#### Answer 3

If two matrices are equal, then their corresponding elements are also equal.

(i)

a + 5 = 2 a = -3

-4 = b + 4 b = -8

2 = c – 1 c = 3

(ii) a= 3

a – b = -1

b = a + 1 = 4

b + c = 2

c = 2 – b = 2 – 4 = -2

#### Question 4

If A = and B = ; find: (i) A + B (ii) B – A

#### Answer 4

#### Question 5

If A=…….., B = ………and C =…….; find:

(i) B + C (ii) A – C

(iii) A + B – C (iv) A – B +C

#### Answer 5

#### Question 6

Wherever possible, write each of the following as a single matrix………………

#### Answer 6

#### Question 7

Find, x and y from the following equations :……………..

#### Answer 7

#### Question 8

Given: M =…………. , find its transpose matrix M^{t}. If possible, find:

(i) M + M^{t} (ii) M^{t} – M

#### Answer 8

#### Question 9

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

Where ……………..

#### Answer 9

#### Question 10

Given ……………………; find the matrix X in each of the following:

(i) X + B = C – A

(ii) A – X = B + C

#### Answer 10

#### Question 11

Given ………………; find the matrix X in each of the following:

(i) A + X = B

(ii) A – X = B

(iii) X – B = A

#### Answer 11

** Chapter-9 Matrices Exercise -9 (B) for Selina Concise Solutions for ICSE Class 10th Mathematics ( Selina Publishers)**

#### Question 1

Evaluate:…………….

#### Answer 1

#### Question 2

Find x and y if:………………

#### Answer 2

#### Question 3

Given ; find:………………….

(i) 2A – 3B + C

(ii) A + 2C – B

#### Answer 3

#### Question 4

If……………..

#### Answer 4

#### Question 5

Given ……………..

(i) find the matrix 2A + B

(ii) find the matrix C such that:

C + B = …………..

#### Answer 5

#### Question 6

If…………… ; find the values of x, y and z.

#### Answer 6

#### Question 7

Given A = ………………and A^{t} is its transpose matrix. Find:

(i) 2A + 3A^{t} (ii) 2A^{t} – 3A

(iii) ………….(iv) …………….

#### Answer 7

#### Question 8

Given ………………..

Solve for matrix X:

(i) X + 2A = B

(ii) 3X + B + 2A = O

(iii) 3A – 2X = X – 2B.

#### Answer 8

#### Question 9

If ………….., show that

3M + 5N = …………..

#### Answer 9

#### Question 10

If I is the unit matrix of order 2 x 2; find the matrix M, such that:

(i) M – 2I = …………

(ii) 5M + 3I =………….

#### Answer 10

#### Question 11

If ………………find matrix M

#### Answer 11

**Chapter 9 – Matrices, Exercise. 9 (C) Concise Solutions (Selina Publishers)**

#### Question 1

Evaluate: if possible:………….

#### Answer 1

#### Question 2

If ………………and I is a unit matrix of order 2 2, find:

(i) AB (ii) BA (iii) AI

(iv) IB (v) A^{2} (vi) B^{2}A

#### Answer 2

#### Question 3

If…………………………………

#### Answer 3

#### Question 4

Find x and y, if:…………………..

#### Answer 4

#### Question 5

If …………., find:

(i) (AB)C (ii) A(BC)

Is A(BC) = (AB)C?

#### Answer 5

#### Question 6

Given ,…………. find; if possible:

(i) AB (ii) BA (iii)A^{2}

#### Answer 6

#### Question 7

If………..find …..

#### Answer 7

#### Question 8

If M = ………….. and I is a unit matrix of the same order as that of M; show that:

M^{2} = 2M + 3I

#### Answer 8

#### Question 9

If …………………. and BA= M^{2}, find the values of a and b.

#### Answer 9

#### Question 10

Given ………………., find:

(i) A – B (ii) A^{2}

(iii) AB (iv) A^{2} – AB + 2B

#### Answer 10

#### Question 11

If ……………….; find:

(i) (A + B)^{2} (ii) A^{2} + B^{2}

(iii) Is (A + B)^{2} = A^{2} + B^{2}?

#### Answer 11

#### Question 12

Find the matrix A…………, if B = and B^{2} = B + ………A.

#### Answer 12

#### Question 13

If A = ………….and A^{2} = I; find a and b.

#### Answer 13

#### Question 14

If ………….; then show that:

(i) A (B + C) = AB + AC

(ii) (B – A)C = BC – AC.

#### Answer 14

#### Question 15

If…………… , simplify:

A^{2} + BC.

#### Answer 15

#### Question 16

Solve for x and y:…………

#### Answer 16

#### Question 17

**In each case given below, find :**

**(a) the order of matrix M.**

**(b) the matrix M.**

(i)………..

(ii)………..

#### Answer 17

#### Question 18

If A= ……….and B=…..Find the value of X given That……….

#### Answer 18

#### Question 19

If A=….., B=……. and C=……..Find AB-5C

Answer 19

Question 20

**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?**

#### Answer 20

AB = BA = B

But it is possible, when A = 0 or B = 0

But B is not a zero matrix (given)

A is a zero matrix or A is an identity matrix

#### Question 21

Given A=………, B=…….. and ThatAB=A+B,Find the value of a,b and c.

#### Answer 21

**Question 22**

If p=…..and Q=…. , then compute:

…………..true for matrix algebra?

#### Answer 22

#### Questions 23

Given the Matrices A=………B=…. and C=……..

find (i)ABC 9ii)ACB state whether ABC=ACB

#### Answer-23

#### Question 24

If A=…,B=….and C=………find each of following if they are equal

(I) CA+B (ii) A+CB

#### Answer 24

From (i) and (II) we can say say that CA+B not equal A+CB

#### Question 25

If A= ….. and B=……Find the matrix of x such that AX=B

#### Answer 25

**Question 26**

If A=…..Find (A-2I)(A-3I)

#### Answer 26

**Question 27**

If A=…. Find:…..Transpose of Matrix A

**Answer 27**

**Question 28**

If M=…..Show That…..Unit Matix

**Answer 28**

#### Question 29

If p=…..and Q=…… find x and y such that PQ=nul matrix.

**Answer 29**

**Question 30**

Evaluate…………….

#### Answer 30

**Question 31.**

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

**(i) A + B = B + A**

**(ii) A – B = B – A**

**(iii) (B . C). A = B . (C . A)**

**………………………**

**(vii) A² – B² = (A + B) (A – B)**

**(viii) (A – B)² = A² – 2 A . B + B²**

**Answer 31**

(i) True : Because addition of matrices is commutative.

(ii) False : Subtraction of matrices is not commutative.

(iii) True : Multiplication of matrices is associative.

(iv) True: Multiplication of matrices is distributive over addition.

(v) True : As given above in (iv)

(vi) True : As given above in (iv)

(vii) False : Laws of algebra for factorization and expansion are not applicable to matrices.

(viii) False, As given above in (vii)

** **

**Exercise 9 (D),Chapter-9 Matrices Concise Maths Solutions Selina Publishers**

**Question 1.**

**Find x and y, if:………….**

**Answer 1**

**Question 2.**

**Find x and y, if :…….**

**Question 3**

If …….find x and y,if (i)…..(ii)…

**Answer 3**

**Question 4**

Given….X=….Write:

**(i) the order of the matrix X**

**(ii) the matrix X.**

#### Answer 4

**Question 5.**

**Evaluate…….**

**Answer 5**

#### Question 6

if A=….,B=…. and 3A x M = 2B, Find Matrix M

**Answer 6**

**Question 7**

If………..find value of a, b, and c.

**Answer 7**

**Question 8**

if A =……… and B =………

**(i) A (BA)**

**(ii) (AB) **

**Answer 8 part (i)**

**Answer 8 part (ii)**

**Question 9**

**Find x and y, if………**

**Answer 9**

**Question 10**

If Matrix X = …… and 2X – 3Y=……..find the matrix X and Matrix Y

**Answer 10**

**Question 11**

Given A=…….B=…. and C=….find Matrix X such that A+X = 2B+C (2005)

**Answer 11**

**Question 12**

Find the Value of x given that ………(2005)

**Answer 12**

**Question 13**

If …., and I is identity matrix of the same order and A^{t} is the transpose of matrix A, find A^{t }.B + BI

**Answer 13**

**Question 14**

Given A = …. B=…. and C=…..find matrix X such that A+2X = 2B+C

#### Answer 14

**Question 15**

Let…………. Find A^{2} – A + BC.

**Answer 15**

**Question 16**

Let A =……… Find A^{2} + AB + B^{2}.

**Answer 16**

#### Question 17

If …………and 3A – 2C = 6B, find the values of a, b and c.

**Answer 17**

**Question 18**

Given A =……………

Find the values of p and q.

**Answer 18**

By comparing,

-2q = -8 q = 4

And p = 8

**Question 19**

Given A = …………. Find AB + 2C – 4D.

**Answer 19**

**Question 20**

Evaluate:…………

**Answer 20**

**Question 21**

**If A=……. I =…… find ……..AxA.-5A+7I**

**Answer 21**

**Question 22**

Given A = ……… And I = ……And …..Find M

**Answer 22**

**Question 23**

**A=……and B=…….if AX = B (2016)**

(i) Write the order of matrix X.

(ii) Find the matrix ‘X’

**Answer 23**

(i) Let the order of matrix X = m × n

Order of matrix A = 2 × 2

Order of matrix B = 2 × 1

Now, AX = B

∴ m = 2 and n = 1

Thus, order of matrix X = m × n = 2 × 1

Multiplying (1) by 2, we get

4x + 2y = 8 ….(3)

Subtracting (2) from (3), we get

3x = 3

⇒ x = 1

Substituting the value of x in (1), we get

2(1) + y = 4

⇒ 2 + y = 4

⇒ y = 2

Hence The Matrix X = x = 1 and y=2

**Question 24**

If A = ……..Find the matrix C where C is a 2 by 2 matrix. (2017)

**Answer 24**

**Question 25**

Given matrix B=…… Find the matrix X if, X = B^{2} – 4B. Hence, solve for a and b given ………..(2017)

**Answer 25**

**—: End of of Matrices Selina Concise Solutions Chapter- 9 :—**

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