2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3

   

Students can Download Maths Chapter 3 Matrices Ex 3.3 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 3.3

2nd PUC Maths Matrices NCERT Text Book Questions and Answers
Ex 3.3

Question 1.
(i)
\(\left[\begin{array}{c}{5} \\{\frac{1}{2}} \\{-1}\end{array}\right]\)
(ii)
\(\left[\begin{array}{cc}{1} & {-1} \\{2} & {3}\end{array}\right]\)
(iii)
\(\left[\begin{array}{ccc}{-1} & {5} & {6} \\{\sqrt{3}} & {5} & {6} \\{2} & {3} & {-1}\end{array}\right]\)
Answer:
Question 2.
\(\mathbf{A}=\left[\begin{array}{ccc}{-1} & {2} & {3} \\{5} & {7} & {9} \\{-2} & {1} & {1}\end{array}\right] \text { and } \mathbf{B}=\left[\begin{array}{ccc}{-4} & {1} & {-5} \\{1} & {2} & {0} \\{1} & {3} & {1}\end{array}\right]\)
then verify that
(i) (A + B)’ = A’ + B’,
(ii) (A – B)’ = A’ – B’
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 1

KSEEB Solutions

Question 3.
\(\mathbf{A}^{\prime}=\left[\begin{array}{rr}{3} & {4} \\{-1} & {2} \\{0} & {1}\end{array}\right] \text { and } \mathbf{B}=\left[\begin{array}{rrr}{-1} & {2} & {1} \\{1} & {2} & {3}\end{array}\right]\)
(i) (A + B)’ = A’ + B’,
(ii) (A – B)’ = A’ – B’
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 2
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 3

Question 4.
If \(A^{\prime}=\left[\begin{array}{cc}{-2} & {3} \\{1} & {2}\end{array}\right] \text { and } B=\left[\begin{array}{cc}{-1} & {0} \\{1} & {2}\end{array}\right]\)
then Find (A + 2B)’
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 4

Question 5.
For the matrices A and B, verify that (AB)’ = B’A’, where
(i)
\(A=\left[\begin{array}{r}{1} \\{-4} \\{3}\end{array}\right], B=\left[\begin{array}{lll}{-1} & {2} & {1}\end{array}\right]\)
(ii)
\(\mathbf{A}=\left[\begin{array}{l}{\mathbf{0}} \\{\mathbf{1}} {\mathbf{2}}\end{array}\right], \mathbf{B}=\left[\begin{array}{lll}{\mathbf{1}} &{\mathbf{5}} & {\mathbf{7}}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 5

KSEEB Solutions

Question 6.
If (i)
\(\mathbf{A}=\left[\begin{array}{cc}{\cos \alpha} & {\sin \alpha} \\{-\sin \alpha} & {\cos \alpha}\end{array}\right]\),then verify that A’ A = 1
(ii)
\(\mathbf{A}=\left[\begin{array}{cc}{\sin \alpha} & {\cos \alpha} \\{-\cos \alpha} & {\sin \alpha}\end{array}\right]\),then verify that A’ A = 1
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 6
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 7

Question 7.
(i) Show that the matrix \(\mathbf{A}=\left[\begin{array}{rrr}{\mathbf{1}} & {\mathbf{1}} & {\mathbf{5}} \\{-\mathbf{1}} & {\mathbf{2}} & {\mathbf{1}} \\{\mathbf{5}} & {\mathbf{1}} & {\mathbf{3}}\end{array}\right]\) is a symmentric matrix.
(ii) Show that the matrix
\(\mathbf{A}=\left[\begin{array}{rrr}{0} & {1} & {-1} \\{-1} & {0} & {1} \\{1} & {-1} & {0}\end{array}\right]\)
is a skew symmentric matrix.
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 8

KSEEB Solutions

Question 8.
For the matrix \(\mathbf{A}=\left[\begin{array}{ll}{\mathbf{1}} & {\mathbf{5}} \\{\mathbf{6}} & {7}\end{array}\right]\) verify that.
(i) ( A + A’) is a symmetric matrix
(ii)(A – A’) is a skew symmetric matrix
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 9
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 10

Question 9.
Find \(\frac{1}{2}\left(A+A^{\prime}\right) \text { and } \frac{1}{2}(A-A)\),when
\(\mathbf{A}=\left[\begin{array}{rrr}{0} & {\mathbf{a}} & {\mathbf{b}} \\{-\mathbf{a}} & {\mathbf{0}} & {\mathbf{c}} \\{-\mathbf{b}} & {-\mathbf{c}} &{\mathbf{0}}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 11

Question 10.
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
(i)
\(\left[\begin{array}{cc}{3} & {5} \\{1} & {-1}\end{array}\right]\)
(ii)
\(\left[\begin{array}{rrr}{6} & {-2} & {2} \\{-2} & {3} & {-1} \\{2} & {-1} & {3}\end{array}\right]\)
(iii)
\(\left[\begin{array}{rrr}{3} & {3} & {-1} \\{-2} & {-2} & {1} \\{-4} & {-5} & {2}\end{array}\right]\)
(iv)
\(\left[\begin{array}{rr}{1} & {5} \\{-1} & {2}\end{array}\right]\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 12
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 13
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 14
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 15
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 16
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 17

KSEEB Solutions

Choose the correct answer in the Exercise 11 and 12.

Question 11.
If A, B are symmetric matrices of same order, then AB – BA is a
(A) Skew symmetric matrix
(B) Symmetric matrix
(C) Zero matrix
(D) Identity matrix
Ans:
A & B are symmetric matrices A’ = A B’ = B
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 18

Question 12.
\(\mathbf{A}=\left[\begin{array}{cc}{\cos \alpha} & {-\sin \alpha} \\{\sin \alpha} & {\cos \alpha}\end{array}\right]\),then A + A’ = I,, if the value of α is
(A) \(\frac{\pi}{6}\)
(B) \(\frac{\pi}{3}\)
(C) π
(D) \(\frac{3 \pi}{2}\)
Answer:
2nd PUC Maths Question Bank Chapter 3 Matrices Ex 3.3 19

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