2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4

Students can Download Maths Chapter 3 Matrices Ex 3.4 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4

2nd PUC Maths Matrices NCERT Text Book Questions and Answers
Ex 3.4

Question 1.
Using elementary transformations, find the inverse of each of the matrices, if it exists
in Exercise 1 to 17
Answer:

2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 1
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 2

Question 2.
\(\left[\begin{array}{ll}{2} & {1} \\{1} & {1}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 3

KSEEB Solutions

Question 3.
\(\left[\begin{array}{ll}{1} & {3} \\{2} & {7}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 4

Question 4.
\(\left[\begin{array}{ll}{2} & {3} \\{5} & {7}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 5

KSEEB Solutions

Question 5.
\(\left[\begin{array}{ll}{2} & {1} \\{7} & {4}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 6
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 7

Question 6.
\(\left[\begin{array}{ll}{2} & {5} \\{1} & {3}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 8

Question 7.
\(\left[\begin{array}{ll}{3} & {1} \\{5} & {2}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 9
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 10

KSEEB Solutions

Question 8.
\(\left[\begin{array}{ll}{4} & {5} \\{3} & {4}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 11

Question 9.
\(\left[\begin{array}{rr}{3} & {10} \\{2} & {7}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 12
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 13

Question 10.
\(\left[\begin{array}{cc}{3} & {-1} \\{-4} & {2}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 14

Question 11.
\(\left[\begin{array}{ll}{2} & {-6} \\{1} & {-2}\end{array}\right]\)
Answer:
A = I A[row transformation]
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 15

Question 12.
\(\left[\begin{array}{rr}{6} & {-3} \\{-2} & {1}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 16
As the matrix on LHS contain 0 only in the second row the given matrix is non-invertible. i.e. A 1 does not exist.

KSEEB Solutions

Question 13.
\(\left[\begin{array}{cc}{2} & {-3} \\{-1} & {2}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 17

Question 14.
\(\left[\begin{array}{ll}{2} & {1} \\{4} & {2}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 18

Question 15.
\(\left[\begin{array}{ccc}{2} & {-3} & {3} \\{2} & {2} & {3} \\{3} & {-2} &{2}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 19
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 20

KSEEB Solutions

Question 16.
\(\left[\begin{array}{rrr}{1} & {3} & {-2} \\{-3} & {0} & {-5} \\{2} & {5} & {0}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 21
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 22

Question 17.
\(\left[\begin{array}{rrr}{2} & {0} & {-1} \\{5} & {1} & {0} \\{0} & {1} & {3}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 23
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.4 24

KSEEB Solutions

Question 18.
Matrices A and B if inverse of each other only W
(A) AB = BA
(B) AB = BA = 0
(C) AB = 0,RA = I
(D) AB = BA = I
Answer:
By definition, A & B me inverses of each other if and only if AB = BA = 1
∴ (D) is the correct answer.

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