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

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## 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

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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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