# 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

Exercise – 9 (A),

Exercise – 9 (B),

Exercise – 9 (C),

Exercise – 9 (D),

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.

(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.

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………….

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

#### Question 5

If A=…….., B =  ………and C =…….; find:

(i) B + C (ii) A – C

(iii) A + B – C (iv) A – B +C

#### Question 6

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

#### Question 7

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

#### Question 8

Given: M =…………. , find its transpose matrix Mt. If possible, find:

(i) M + Mt (ii) Mt – M

#### Question 9

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

Where ……………..

#### Question 10

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

(i) X + B = C – A

(ii) A – X = B + C

#### Question 11

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

(i) A + X = B

(ii) A – X = B

(iii) X – B = A

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

Evaluate:…………….

#### Question 2

Find x and y if:………………

#### Question 3

Given ; find:………………….

(i) 2A – 3B + C

(ii) A + 2C – B

If……………..

#### Question 5

Given ……………..

(i) find the matrix 2A + B

(ii) find the matrix C such that:

C + B = …………..

#### Question 6

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

#### Question 7

Given A =  ………………and At is its transpose matrix. Find:

(i) 2A + 3At (ii) 2At – 3A

(iii)  ………….(iv) …………….

#### Question 8

Given ………………..

Solve for matrix X:

(i) X + 2A = B

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

(iii) 3A – 2X = X – 2B.

#### Question 9

If ………….., show that

3M + 5N = …………..

#### 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 =………….

#### Question 11

If ………………find matrix M

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

#### Question 1

Evaluate: if possible:………….

#### Question 2

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

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

(iv) IB (v) A2 (vi) B2A

If…………………………………

#### Question 4

Find x and y, if:…………………..

#### Question 5

If  …………., find:

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

Is A(BC) = (AB)C?

#### Question 6

Given  ,…………. find; if possible:

(i) AB (ii) BA (iii)A2

If………..find …..

#### Question 8

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

M2 = 2M + 3I

#### Question 9

If …………………. and BA= M2, find the values of a and b.

#### Question 10

Given ………………., find:

(i) A – B (ii) A2

(iii) AB (iv) A2 – AB + 2B

#### Question 11

If ……………….; find:

(i) (A + B)2 (ii) A2 + B2

(iii) Is (A + B)2 = A2 + B2?

#### Question 12

Find the matrix A…………, if B = and B2 = B + ………A.

#### Question 13

If A =  ………….and A2 = I; find a and b.

#### Question 14

If ………….; then show that:

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

(ii) (B – A)C = BC – AC.

#### Question 15

If…………… , simplify:

A2 + BC.

#### Question 16

Solve for x and y:…………

#### Question 17

In each case given below, find :
(a) the order of matrix M.
(b) the matrix M.

(i)………..

(ii)………..

#### Question 18

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

#### Question 19

If A=….., B=……. and C=……..Find AB-5C

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?

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.

#### Question 22

If p=…..and Q=…. , then compute:

…………..true for matrix algebra?

#### Questions 23

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

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

#### Question 24

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

(I) CA+B  (ii) A+CB

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

Question 26

If A=…..Find (A-2I)(A-3I)

#### Question 27

If A=…. Find:…..Transpose of Matrix A

#### Question 28

If M=…..Show That…..Unit Matix

#### Question 29

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

#### Question 30

Evaluate…………….

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

(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:………….

#### Question 2.

Find x and y, if :…….

#### Question 3

If …….find x and y,if (i)…..(ii)…

#### Question 4

Given….X=….Write:

(i) the order of the matrix X
(ii) the matrix X.

Question 5.

Evaluate…….

#### Question 6

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

#### Question 7

If………..find value of a, b, and c.

#### Question 8

if A =………  and B =………
(i) A (BA)
(ii) (AB)

#### Question 9

Find x and y, if………

#### Question 10

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

#### Question 11

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

#### Question 12

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

#### Question 13

If …., and I is identity matrix of the same order and At is the transpose of matrix A, find A.B + BI

#### Question 14

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

#### Question 15

Let…………. Find A2 – A + BC.

#### Question 16

Let A =……… Find A2 + AB + B2.

#### Question 17

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

#### Question 18

Given A =……………

Find the values of p and q.

By comparing,

-2q = -8  q = 4

And p = 8

#### Question 19

Given A = …………. Find AB + 2C – 4D.

Evaluate:…………

#### Question 21

If A=……. I =…… find ……..AxA.-5A+7I

#### Question 22

Given A = ……… And I = ……And …..Find M

#### Question 23

A=……and B=…….if AX = B     (2016)

(i) Write the order of matrix X.

(ii) Find the matrix ‘X’

(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)

#### Question 25

Given matrix B=…… Find the matrix X if, X = B2 – 4B. Hence, solve for a and b given ………..(2017)

### Chapter Wise Concise Maths Solutions for ICSE Class 10th

1. GST ( Goods and Services Tax)
2. Banking
3. Shares and Dividends
4. Linear In equations in One Variable
6. Solving Simple Problems (Based on Quadratic Equations)
7. Ratio and Proportion ( Including Properties and Uses )
8. Reminder and Factor Theorems
9. Matrices ( Currently Open)
10. Arithmetic Progression
11. Geometric Progression
12. Reflection
13. Section And Mid Point Formula
14. Equation of a Line
15. Similarity (With Applications to Maps and Models )
16. Loci (Locus and its Constructions)
17. Circles
18. Tangents and Intersecting Chords
19. Constructions ( Circles)
20. Cylinder, Cone and Spheres (Surface Area and Volume )
21. Trigonometrical Identities
22. Heights and Distances
23. Graphical Representation (Histograms and Ogives)
24. Measures of Central Tendency (Mean , Median, Quartiles and Mode)
25. Probability

### Other Subject Chapter-Wise Solution for ICSE

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