Show that the matrix A , where A = 1 - 1 5 - 1 2 1 5 1 3 is a symmetric matrix.

Given that, A = 1 - 1 5 - 1 2 1 5 1 3 To proof : It is a symmetric matrix Now, Matrix is said to be symmetric if A = A T So, A T = 1 - 1 5 - 1 2 1 5 1 3 Therefore, A = A T , Hence A is symmetric matrix.

Define a symmetric matrix. Prove that for A = 2 4 5 6 , A + A ' is a symmetric.

Definition of symmetric matrix : If transpose of the matrix is equal to itself, that is called symmetric matrix. i.e. A ' = A and B ' = B . Given that, A = 2 4 5 6 To proof : A + A ' is a symmetric Now, A + A ' = 2 4 5 6 + 2 5 4 6 A + A ' = 2 + 2 4 + 5 5 + 4 6 + 6 A + A ' = 4 9 9 12 A + A ' ' = 4 9 9 12 [definition of matrix] Hence, A + A ' = A + A ' ' .

If A = 2 3 4 5 , Prove that A - A T is a skew-symmetric matrix.

Given that, A = 2 3 4 5 To Proof : A - A T is a skew-symmetric matrix . Now, A = 2 3 4 5 A T = 2 4 3 5 A - A T = 2 3 4 5 - 2 4 3 5 A - A T = 0 - 1 1 0 A - A T T = 0 1 - 1 2 or, A - A T T = - 0 - 1 1 0 = - A - A T Hence, it is a skew-symmetric matrix.

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Understanding ISC Mathematics Class 12 Volume 1>Chapter 3 - Matrices>EXERCISE 3.4

M L Aggarwal Solutions for Chapter: Matrices, Exercise 4: EXERCISE 3.4

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Matrices, Exercise 4: EXERCISE 3.4

Attempt the practice questions on Chapter 3: Matrices, Exercise 4: EXERCISE 3.4 with hints and solutions to strengthen your understanding. Understanding ISC Mathematics Class 12 Volume 1 solutions are prepared by Experienced Embibe Experts.