NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3 Matrices
NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3: Get inside detail NCERT Solutions for Class 12 Maths Chapter 3-Matrices Exercise 3.3 prepared by academic team of Physics Wallah all questions are solved in detail
Krati Saraswat10 Jan, 2024
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NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3 Matrices
NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3 Matrices is prepared by academic team of Physics Wallah. We have prepared NCERT Solutions for all exercise of chapter 3. Given below is step by step solutions of all questions given in NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3 Matrices.NCERT Solutions for Class 12 Maths Chapter 3 Miscellaneous Exercise
NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3
Solve The Following Questions NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.3 Matrices
Question 1. Find the transpose of each of the following matrices: (i)
(ii)
(iii)
Solution :
(i) Let A =
Transpose of A = A’ or A
T
= [ 5 1/2 -1]
(ii)
Transpose of A = A’ or A
T
=
(iii)
Transpose of A = A’ or A
T
=
NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.1
Question 2. If
then verify that:
(i)
(A + B)' = A' + B'
(ii)
(A - B)' = A' - B'
Solution :
NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.2
Question 3. If
then verify that:
(i)
(A + B)' = A' + B'
(ii)
(A - B)' = A' - B'
Solution :
NCERT Solutions for Class 12 Maths Chapter 3 Exercise 3.4
Question 4. If
then find (A + 2B)’.
Solution :
(ii)
Solution :
| NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1 | NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.2 |
| NCERT Solutions for Class 12 Maths Chapter 2 Miscellaneous Exercise | |
then verify that A’A = I.
(ii) If A =
then verify that A’A = I.
Solution :
Question
7. (i) Show that the matrix A =
is a symmetric matrix.
(ii) Show that the matrix A =
is a skew symmetric matrix.
Solution :
(i) Given: A =
Changing rows of matrix A as the columns of new matrix A’ =
= A
∴ A’ = A
Therefore, by definitions of symmetric matrix, A is a symmetric matrix.
(ii) Given: A =
A’ =
=
-
= - A
∴ A’ = - A
Therefore, by definition matrix A is a skew-symmetric matrix
Question
8. For a matrix A =
verify that:
(i) (A + A’) is a symmetric matrix.
(ii) (A – A’) is a skew symmetric matrix.
Solution :
Question
9. Find 1/2 (A + A’) and 1/2(A – A’) when A =
Solution :
Question
10. Express the following matrices as the sum of a symmetric and skew symmetric matrix:
(i)
(ii)
(iii)
(iv)
Solution :
.png)
(iii)
(iv)
Choose the correct answer in Exercises 11 and 12.
Question 11. If A and B are symmetric matrices of same order, AB – BA is a: (A) Skew-symmetric matrix (B) Symmetric matrix (C) Zero matrix (D) Identity matrix Solution : Given: A and B are symmetric matrices ∴ A = A’ and B = B’ Now, (AB – BA)’ = (AB)’ – (BA)’ ∴ (AB – BA)’ = B’A’ – A’B’ [Reversal law] ∴ (AB – BA)’ = BA – AB [From eq. (i)] ∴ (AB – BA)’ = – (AB – BA) ∴ (AB – BA) is a skew matrix. Therefore, option (A) is correct. Question 12. If A =
, then A + A’ = I, if the value of
α is:
(A) π/6
(B) π/3
(C)
π
(D) 3
π/2
Solution :
Therefore, option (B) is correct.
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