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# Frank solutions for Class 10 Mathematics chapter 11 - Matrices

## Chapter 11: Matrices

Exercise 11.1Exercise 11.2

#### Chapter 11: Matrices Exercise Exercise 11.1 solutions [Page 0]

Classify the following rnatrix :

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

Classify the following matrix :

[(7, 0)]

Classify the following matrix :

|(800),(521)|

Classify the following matrix :

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

Classify the following matrix :

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

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

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

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)|

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

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

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

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

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

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

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

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

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

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

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

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

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

If A = |(1,9,4),(5 , 0 , 3)|  find A'

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

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

If P = |(8,5),(7,2)| find  P - Pt

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.

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

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.

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

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.

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

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

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

#### Chapter 11: Matrices Exercise Exercise 11.2 solutions [Page 0]

Evaluate the following :

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

Evaluate the following:

|(3 , 2)|  |(-1) , (3)|

Evaluate the following :

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

Evaluate the following :

|(1 , 1),(2 , 3)|  |(2 , 1),(1 , 4)|

Evaluate the following :

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

Evaluate the following :

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

Evaluate the following :

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

Evaluate the following :

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

Evaluate the following :

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

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

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

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.

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

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

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

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

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.

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) ?

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

## Chapter 11: Matrices

Exercise 11.1Exercise 11.2

## Frank solutions for Class 10 Mathematics chapter 11 - Matrices

Frank solutions for Class 10 Maths 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 Frank 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 Class 10 Mathematics chapter 11 Matrices are Introduction to Matrices, Addition and Subtraction of Matrices, Multiplication of Matrix, Matrices Examples.

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