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.
Board | CBSE |
Textbook | NCERT |
Class | Class 12 |
Subject | Maths |
Chapter | Chapter 3 |
Chapter Name | Matrices |
Exercise | Ex 3.3 |
Number of Questions Solved | 12 |
Category | NCERT 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 =
∴ transpose of A = A’ =
Ex 3.3 Class 12 Maths Question 2.
If
then verify that:
(i) (A+B)’=A’+B’
(ii) (A-B)’=A’-B’
Solution:
Ex 3.3 Class 12 Maths Question 3.
If
then verify that:
(i) (A+B)’ = A’+B’
(ii) (A-B)’ = A’-B’
Solution:
Ex 3.3 Class 12 Maths Question 4.
If
then find (A+2B)’
Solution:
Ex 3.3 Class 12 Maths Question 5.
For the matrices A and B, verify that (AB)’ = B’A’, where
Solution:
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)
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,
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:
=>
Ex 3.3 Class 12 Maths Question 9.
Find and ,when
Solution:
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
=>
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
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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