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# Frank solutions for ICSE Class 10 Mathematics Part 2 chapter 11 - Matrices [Latest edition]

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#### Chapters ## Chapter 11: Matrices

Exercise 11.1Exercise 11.2

### Frank solutions for ICSE Class 10 Mathematics Part 2 Chapter 11 Matrices Exercise 11.1

Exercise 11.1 | Q 1.1

Classify the following rnatrix :

|(2,1),(0 , 6),(8 , 7) |

Exercise 11.1 | Q 1.2

Classify the following matrix :

[(7, 0)]

Exercise 11.1 | Q 1.3

Classify the following matrix :

|(800),(521)|

Exercise 11.1 | Q 1.4

Classify the following matrix :

|(1 , 1),(0,9)|

Exercise 11.1 | Q 1.5

Classify the following matrix :

|(11 , 3 , 0),(21 , 8 , 4),(15,5,2)|

Exercise 11.1 | Q 2

Find the values of a and b) if [2a + 3b a - b] = [19  2].

Exercise 11.1 | Q 3

Find the values of x and y, if  |(3"x" - "y"),(5)| = |(7) , ("x + y")|

Exercise 11.1 | Q 4

Find the values of a, b, c and d, if |("a + 3b", 3"c" + "d"),(2"a" - "b" , "c" - 2"d")| = |(5 , 8),(3 , 5)|

Exercise 11.1 | Q 5.1

If A = |(1215),(1117)| and B = |(2,7),(4,9)| , find :  A + B

Exercise 11.1 | Q 5.2

If A = |(1215),(1117)| and B = |(2,7),(4,9)| find : 2A + 3B

Exercise 11.1 | Q 5.3

If A = |(1215),(1117)| and B = |(2,7),(4,9)| find A - 2B

Exercise 11.1 | Q 6.1

If A = [4  7] and B = [3 1] , find:  A+2B

Exercise 11.1 | Q 6.2

If A = [4 7] and B = [3 l], find:  A - B

Exercise 11.1 | Q 6.3

If A = [4 7] and B = [3 l], find : 2A - 3B

Exercise 11.1 | Q 7.1

If P = |(2 , 9),(5 , 7)| and Q = |(7 , 3),(4 , 1)| , find 2P + 3Q

Exercise 11.1 | Q 7.2

If P =|(2,9),(5,7)| and Q = |(7,3),(4,1)| find  2Q - P

Exercise 11.1 | Q 7.3

If P = |(2,9),(5 , 7)| and Q = |(7 , 3),(4 , 1)| find 3P - 2Q

Exercise 11.1 | Q 8

If A = |(17 , 5 , 19),(11 , 8 , 13)|  and B =|(9,3,7),(1,6,5)| , find 2A - 3B

Exercise 11.1 | Q 9.1

If M = |(8,3),(9,7),(4,3)|  and N = |(4,7),(5,3),(10 , 1)|  find M+N

Exercise 11.1 | Q 9.2

If M =|(8,3),(9,7),(4,3)| and N = |(4,7),(5,3),(10,1)| find M - N

Exercise 11.1 | Q 10.1

If A =|(1, 9 , 4),(5 , 0 , 3)| , find negative A

Exercise 11.1 | Q 10.2

If A = |(1,9,4),(5 , 0 , 3)|  find A'

Exercise 11.1 | Q 11.1

If P = (8 , 5),(7 , 2) , find Pt

Exercise 11.1 | Q 11.2

If P= (8,5),(7,2) find : P + Pt

Exercise 11.1 | Q 11.3

If P = |(8,5),(7,2)| find  P - Pt

Exercise 11.1 | Q 12

If B = |(15 , 13),(11,12),(10,17)| , find the transpose of matrix Band If possible find the sum of the two matrices. If not possible state the reason.

Exercise 11.1 | Q 13

If A = |(5,"r"),("p",7)| , c and if A + B = (9,7),(5,8) , find the values of p,q,r and s.

Exercise 11.1 | Q 14

If A = |("p","q"),(8,5)| , B = |(3"p",5"q"),(2"q" , 7)| and if A + B = |(12,6),(2"r" , 3"s")| , find the values of p,q,r and s.

Exercise 11.1 | Q 15

If |(2"a" + "b" , "c"),("d" , 3"a" - "b")| = |(4 , 3"a"),(7 , 6)| , find the values of a , b , c and d.

Exercise 11.1 | Q 16

If |(3"a" + 2"b" , 2"a" - "b"),(4"p" - 3"q" , 2"p" + "q")| = |(12 , 1),(16 , 8)| , find the values of a , b , p and q.

Exercise 11.1 | Q 17.1

If A = |(15,7),(13,8)| and B = |(16 , 12),(27,11)| , find matrix X such that  A + X

Exercise 11.1 | Q 17.2

If A = |(15,7),(13,8)| and B = |(16,12),(27,11)|,  find matrix X such that 2A - X = B.

Exercise 11.1 | Q 18

If P = |(14 , 17),(13,1)| and Q = |(2 , 1),(3 , -3)| , find matrix M such that P - M = 3Q

### Frank solutions for ICSE Class 10 Mathematics Part 2 Chapter 11 Matrices Exercise 11.2

Exercise 11.2 | Q 1.1

Evaluate the following :

|(-2 , 3),(-1 , 4)| |(6 , 4),(3 ,- 1)|

Exercise 11.2 | Q 1.2

Evaluate the following:

|(3 , 2)|  |(-1) , (3)|

Exercise 11.2 | Q 1.3

Evaluate the following :

|(2 , -5),(0 , -3)| |(1 , -1),(3 , 2)|

Exercise 11.2 | Q 1.4

Evaluate the following :

|(1 , 1),(2 , 3)|  |(2 , 1),(1 , 4)|

Exercise 11.2 | Q 1.5

Evaluate the following :

|(2 , 3),(-4 , 0)| |(3 , -2),(-1 , 4)|

Exercise 11.2 | Q 1.6

Evaluate the following :

|(2,1) ,(3,2),(1 , 1)|  |(1 , -2 , 1),(2 , 1 , 3)|

Exercise 11.2 | Q 1.7

Evaluate the following :

|(0 , 1),(-1 , 2),(-2 , 0)|  |(0 , -4 , 0),(3 , 0 , -1)|

Exercise 11.2 | Q 1.8

Evaluate the following :

|(6 , 1),(3 , 1),(2 , 4)|  |(1 , -2 , 1),(2 , 1 , 3)|

Exercise 11.2 | Q 1.9

Evaluate the following :

|(0 , 1 , 0),(2 , 0 , -3),(1 , 0 , -2)|  |(1 , -2),(3 , 4),(0 , 0)|

Exercise 11.2 | Q 2.1

If A = |(1,3),(3,2)| and B = |(-2,3),(-4,1)|   find AB

Exercise 11.2 | Q 2.2

If A = |(1,3),(3,2)| and B = |(-2 , 3),(-4 , 1)|  find BA

Exercise 11.2 | Q 3

Let A be a 2 x 2 matrix and let I be an identity matrix of the order 2 x 2. Prove that AI = IA = A.

Exercise 11.2 | Q 4

If P = |(1 , 2),(2 , 1)| and Q = |(2 , 1),(1 , 2)| find P (QP).

Exercise 11.2 | Q 5.1

If P =|(1 , 2),(3 , 4)| , Q = |(5 , 1),(7 , 4)| and R = |(2 , 1),(4 , 2)|  find the value of  P(Q + R)

Exercise 11.2 | Q 5.2

If P =|(1 , 2),(3 , 4)| , Q = |(5 , 1),(7 , 4)| and R = |(2 , 1),(4 , 2)|   find the value of  (R + Q)P

Exercise 11.2 | Q 6

If X = |(1 , -2),(1 , 3)| , Y = |(-3 , 0),(4 , 1)| and Z = |(5 , -1),(3 , 2)| , prove that X (Y + Z) = XY + XZ

Exercise 11.2 | Q 7

If A = |(3,-2),(-1 , 4)| , B = |(2"a"),(1)| , C = |(-4),(5)| , D = |(2),("b")| and AB + 2C = 4D then find the values of a and b.

Exercise 11.2 | Q 8.1

Let A = |(3 , 2),(0 ,5)| and B = |(1 ,0),(1 ,2)| , find (i) (A + B)(A - B)  (ii) A2 - B2 . Is (i) equal to (ii) ?

Exercise 11.2 | Q 9

Find X and Y , if |(1,2),(2 , -3)|  |(x),(y)| = |(-1) , (12)|

## Chapter 11: Matrices

Exercise 11.1Exercise 11.2 ## Frank solutions for ICSE Class 10 Mathematics Part 2 chapter 11 - Matrices

Frank solutions for ICSE Class 10 Mathematics Part 2 chapter 11 (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 ICSE Class 10 Mathematics Part 2 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in ICSE Class 10 Mathematics Part 2 chapter 11 Matrices are Introduction to Matrices, Addition and Subtraction of Matrices, Multiplication of Matrix, Matrices Examples.

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