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Maths Assignment Class 12 Chapter 3 | Matrices

Mathematics Assignment Class 12 

Chapter 3 | Matrices 

Mathematics assignment for class XII chapter 3, Extra questions with answer key on chapter 3 matrices strictly according to the CBSE syllabus and very useful for examinations.

Mathematics Assignment On Matrices
Class XII Chapter 3 

Strictly according to the CBSE Syllabus

Question 1

For the matrix A =  , find   (A - A'), where A' is the transpose of matrix A.

Ans:   

Question 2

Construct a 2 x 3 matrix whose elements in the ith row and the jth column are given by   .

Ans: 

Question 3

Find a matrix X such that 2A + B + X = 0, where

A =    B = 

Ans:  

Question 4

If A =  , find k such that   A2 = KA – 2I

Ans:  K = 1

Question 5

Solve for x and y ;    = 

Ans: x = 5, y = 3

Question 6

If A =  , find a matrix B such that AB = I

Ans:  

Question 7

If B is a skew symmetric matrix, write whether the matrix (ABA') is symmetric or skew symmetric matrix

Ans: Skew symmetric matrix

Question 8

Show that matrix B'AB is symmetric or skew symmetric according as A is symmetric or skew symmetric matrix.

Question 9

Simplify:    +  

Ans:  

Question 10

If A =   , find x, 0 < x < π/2  , when A + A' = I

Ans:  x = π / 3

Question 11

Let A =  , express A as sum of two matrices such as one is symmetric and other is skew symmetric.

Ansswer

equation
Question 12

If  A =   , find  A2 – 5A +4I and hence find a matrix X such that A2 – 5A + 4I + X = 0

Ans:  

Question 13

If A =  , then show that A2 – 4A - 5I = O and hence find A-1

Ans:  A-1 =  
Question 14
Find the value of x - y ; if 2  +  = 
Answer : 0 or zero

Question 15:
If A =   and  B =  , then find the value X such that  2A + X = 5B

Answer:  X = equation
Question 16

If    =  , Find x

Ans: x = 13

Question 17
If      = 0 , find  x

Answer : x = -2, x = -1
Question 18

If  =  , then find the value of y

Answer: y = 2
Question 19

If  A =  , then Evaluate :  - 4A + 3I

Answer : 
Question 20
If A = [aij] is a square matrix of order 2 such that 
equation
then find the value of A2   
Answer:

equation

Question: 21

equation

Answer: equation

Question 22

equation  , then  find (AB)T
Answer:

equation

Question 23
If     equation   then find the value of Z
Answer: 1

Question 24
Check whether the following matrix is an orthogonal or not

equation

Answer: Yes it is an orthogonal matrix

Solution Hint

A matrix is said to be orthogonal if   AA’ = I

Question 25
What must be the matrix   X,  if equation 
Answer: equation

Question 26
Find x and y , if A = equation , B = equation and (A + B)2 = A2 + B2 
Answer : x = 1, y = 4
Solution Hint
Solve the equation (A +B)2 = A2 + B2 we get
AB + BA = 0
Now in this equation putting the values of matrices A and B and comparing the corresponding terms we get the values of x and y. 

Question 27
Verify that the matrix A = equation  is the inverse of B = equation 
Solution Hint 
Find the product AB, If AB = I then A is the inverse of B or B is the inverse of A

Question 28
Three schools X, Y, Z organized a fate (mela) for collecting funds for good victims in which they sold hand-held fans, mats and toys made from recycled material, the sale price of each being Rs 25, Rs 100 and Rs 50 respectively. The following table shows the number of articles of each type sold.

   School 

Article 

X

Y

Z

Hand-Held Fans

Mats

Toys

30

12

70

40

15

55

35

20

75


Using matrices, find the funds collected by each school by selling the above articles and the total funds collected.

Ans: Funds collected by school X = ₹ 5450
Funds collected by school Y = ₹ 5250
Funds collected by school Z = ₹ 6625
Total fund collected = ₹ 17325

THANKS FOR YOUR VISIT
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