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 1For the matrix A = , find (A  A'), where A' is the transpose of matrix A.
Answer:
Question 2Construct a 2 x 3 matrix whose elements in the ith row and the jth column are given by .
Answer:
Question 3Find a matrix X such that 2A + B + X = 0, where
A = B =
Ans:
Question 4If A = , find k such that A^{2}
= KA – 2I
Ans: K = 1
Question 5Solve for x and y ; =
Ans: x = 5, y = 3
Question 6If A = , find a matrix B such that AB = I
Ans:
Question 7If B is a skew symmetric matrix, write whether the matrix (ABA') is symmetric or skew symmetric matrix
Ans: Skew symmetric matrix
Question 8Show that matrix B'AB is symmetric or skew symmetric according as A is symmetric or skew symmetric matrix.
Question 9Simplify: +
Ans:
Question 10If A = , find x, 0 < x < Ï€/2 , when A + A' = I
Ans: x = Ï€ / 3
Question 11Let A = , express A as sum of two matrices such as one is symmetric and other is skew symmetric.
Ansswer
Question 12If A = , find A^{2} – 5A +4I
and hence find a matrix X such that A^{2} – 5A + 4I + X = 0
Ans:
Question 13If A = , then show that A^{2} – 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 =
Question 16
Ans: x = 13
Question 17
Answer : x =  2, x =  1
Question 18
If = , then find the value of y
Answer: y = 2
If A = , then Evaluate : A^{2 } 4A + 3I Answer : Question 20
If A = [a_{ij}] is a square matrix of order 2 such that
then find the value of A^{2}
Answer:
Question: 21
Answer : Question 22
, then find (AB)^{T} Answer:
Question 23
If then find the value of Z Answer: 1
Question 24
Check whether the following matrix is an orthogonal or not
Answer: Yes it is an orthogonal matrixSolution Hint
A matrix is said to be orthogonal if AA' = I
Question 25
What must be the matrix X, if Answer:
Question 26
Find x and y , if A = , B = and (A + B)^{2} = A^{2} + B^{2}
Answer : x = 1, y = 4
Solution Hint
Solve the equation (A +B)^{2} = A^{2} + B^{2} 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 = is the inverse of B = 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
, find the value of (a + x)  (b + y)
Answer: (a + x)  (b + y) = (1 + 3)  (5  4) = 3
Question 29
If is a scalar matrix then find the value of a + 2b + 3c + 4d
Answer: 25
Solution Hint: Scalar matrix is a matrix whose diagonal elements are equal and non diagonal elements are zero.
Question 30
If is a skew symmetric matrix then find the value of 2a  (b + c)
Answer: 0
Solution Hint:
For skew symmetric matrices
All diagonal elements are zero.
Corresponding Elements on the either side of the diagonal are equal but with opposite sign.
Question 31
Three schools X, Y, Z organized a fate (mela) for collecting funds for good victims in which they sold handheld 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

HandHeld
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
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