NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3

In this chapter, we provide NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3 for English medium students, Which will very helpful for every student in their exams. Students can download the latest NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3 pdf, free NCERT solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3 book pdf download.

BoardCBSE
TextbookNCERT
ClassClass 12
SubjectMaths
ChapterChapter 3
Chapter NameMatrices
ExerciseEx 3.3
Number of Questions Solved12
CategoryNCERT Solutions

NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3

Ex 3.3 Class 12 Maths Question 1.
Find the transpose of each of the following matrices:
(i)
(ii)
(iii)
Solution:
(i) let A = left[ begin{matrix} 5 \ frac { 1 }{ 2 } \ -1 end{matrix} right]
∴ transpose of A = A’ = left[ begin{matrix} 5 & frac { 1 }{ 2 } & -1 end{matrix} right]
NCERT Solutions for Class 12 Maths Chapter 3 Matrices 1

Ex 3.3 Class 12 Maths Question 2.
If
then verify that:
(i) (A+B)’=A’+B’
(ii) (A-B)’=A’-B’
Solution:
A=left[ begin{matrix} -1 & 2 & 3 \ 5 & 7 & 9 \ -2 & 1 & 1 end{matrix} right] ,B=left[ begin{matrix} -4 & 1 & -5 \ 1 & 2 & 0 \ 1 & 3 & 1 end{matrix} right]
NCERT Solutions for Class 12 Maths Chapter 3 Matrices 2
NCERT Solutions for Class 12 Maths Chapter 3 Matrices 2.1

Ex 3.3 Class 12 Maths Question 3.
If
then verify that:
(i) (A+B)’ = A’+B’
(ii) (A-B)’ = A’-B’
Solution:
A'=left[ begin{matrix} 3 & 4 \ -1 & 2 \ 0 & 1 end{matrix} right] ,B=left[ begin{matrix} -1 & 2 & 1 \ 1 & 2 & 3 end{matrix} right]
NCERT Solutions for Class 12 Maths Chapter 3 Matrices 3
byjus class 12 maths Chapter 3 Matrices 3.1

Ex 3.3 Class 12 Maths Question 4.
If
then find (A+2B)’
Solution:
A'=begin{bmatrix} -2 & 3 \ 1 & 2 end{bmatrix},B=begin{bmatrix} -1 & 0 \ 1 & 2 end{bmatrix}
NCERT Solutions for Class 12 Maths Chapter 3 Matrices 4

Ex 3.3 Class 12 Maths Question 5.
For the matrices A and B, verify that (AB)’ = B’A’, where


Solution:
(i)quad A=left[ begin{matrix} 1 \ -4 \ 3 end{matrix} right]
A'=left[ begin{matrix} 1 & -4 & 3 end{matrix} right]
NCERT Solutions for Class 12 Maths Chapter 3 Matrices 5
NCERT Solutions for Class 12 Maths Chapter 3 Matrices 5.1
NCERT Solutions for Class 12 Maths Chapter 3 Matrices 5.2

Ex 3.3 Class 12 Maths Question 6.
If (i) ,the verify that A’A=I
If (ii) ,the verify that A’A=I
Solution:
(i) A=begin{bmatrix} sinalpha & quad cosalpha \ -sinalpha & quad cosalpha end{bmatrix}
A'=begin{bmatrix} cosalpha & quad -sinalpha \ sinalpha & quad cosalpha end{bmatrix}
byjus class 12 maths Chapter 3 Matrices 6

Ex 3.3 Class 12 Maths Question 7.
(i) Show that the matrix is a symmetric matrix.
(ii) Show that the matrix is a skew-symmetric matrix.
Solution:
(i) For a symmetric matrix aij = aji
Now,
A=left[ begin{matrix} 1 & -1 & 5 \ -1 & 2 & 1 \ 5 & 1 & 3 end{matrix} right]
NCERT Solutions for Class 12 Maths Chapter 3 Matrices 7

Ex 3.3 Class 12 Maths Question 8.
For the matrix,
(i) (A+A’) is a symmetric matrix.
(ii) (A-A’) is a skew-symmetric matrix.
Solution:
A=begin{bmatrix} 1 & 5 \ 6 & 7 end{bmatrix}
=> A'=begin{bmatrix} 1 & 6 \ 5 & 7 end{bmatrix}
NCERT Solutions for Class 12 Maths Chapter 3 Matrices 8
NCERT Solutions for Class 12 Maths Chapter 3 Matrices 8.1

Ex 3.3 Class 12 Maths Question 9.
Find and ,when

Solution:
A=left[ begin{matrix} 0 & a & b \ -a & 0 & c \ -b & -c & 0 end{matrix} right]
A'=left[ begin{matrix} 0 & -a & -b \ a & 0 & -c \ b & c & 0 end{matrix} right]
byjus class 12 maths Chapter 3 Matrices 9

Ex 3.3 Class 12 Maths Question 10.
Express the following matrices as the sum of a symmetric and a skew-symmetric matrix.
(i)
(ii)
(iii)
(iv)
Solution:
(i) let A=begin{bmatrix} 3 & 5 \ 1 & -1 end{bmatrix}
=> A'=begin{bmatrix} 3 & 1 \ 5 & -1 end{bmatrix}
NCERT Solutions for Class 12 Maths Chapter 3 Matrices 10
NCERT Solutions for Class 12 Maths Chapter 3 Matrices 10.1
NCERT Solutions for Class 12 Maths Chapter 3 Matrices 10.2
byjus class 12 maths Chapter 3 Matrices 10.3
NCERT Solutions for Class 12 Maths Chapter 3 Matrices 10.4
NCERT Solutions for Class 12 Maths Chapter 3 Matrices 10.5

Ex 3.3 Class 12 Maths Question 11.
Choose the correct answer in the following questions:
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
Solution:
Now A’ = B, B’ = B
(AB-BA)’ = (AB)’-(BA)’
= B’A’ – A’B’
= BA-AB
= – (AB – BA)
AB – BA is a skew-symmetric matrix Hence, option (a) is correct.

Ex 3.3 Class 12 Maths Question 12.
If then A+A’ = I, if the
value of α is
(a)
(b)
(c) π
(d)
Solution:
Now
byjus class 12 maths Chapter 3 Matrices 12
Thus option (b) is correct.

All Chapter NCERT Solutions For Class12 Maths

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All Subject NCERT Solutions For Class12

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