If A = 5 - 1 - 2 6 , determine whether A - A ' is symmetric or skew-symmetric.

Given that, A = 5 - 1 - 2 6 We need to find whether A - A ' is symmetric or skew-symmetric Now, A - A ' = 5 - 1 - 2 6 - 5 - 2 - 1 6 A - A ' = 5 - 5 - 1 + 2 - 2 + 1 6 - 6 A - A ' = 0 1 - 1 0 Let, P = A - A ' = 0 1 - 1 0 P ' = 0 - 1 1 0 = - 0 1 - 1 0 = - P Hence, A - A ' is skew-symmetric matrix.

If A = 5 - 1 - 2 6 , determine whether A - A ' is symmetric or skew-symmetric.

Given that, A = 5 - 1 - 2 6 We need to find whether A - A ' is symmetric or skew-symmetric Now, A - A ' = 5 - 1 - 2 6 - 5 - 2 - 1 6 A - A ' = 5 - 5 - 1 + 2 - 2 + 1 6 - 6 A - A ' = 0 1 - 1 0 Let, P = A - A ' = 0 1 - 1 0 P ' = 0 - 1 1 0 = - 0 1 - 1 0 = - P Hence, A - A ' is skew-symmetric matrix.

If A = 5 a b 0 and A is symmetric matrix, Show that a = b .

It is given that, A = 5 a b 0 and A is symmetric matrix We need to prove: a = b Now, A = A ' [symmetric] 5 a b 0 = 5 a b 0 ' 5 a b 0 = 5 b a 0 Equating the corresponding elements we get, a = b Hence, a = b .

If the matrix 6 - x 2 2 x - 15 10 is symmetric, find the value(s) of x .

It is given that, Matrix 6 - x 2 2 x - 15 10 is symmetric We need to find : value(s) of x Now, A ' = A [symmetric] 6 2 x - 15 - x 2 10 = 6 - x 2 2 x - 15 10 Equating the corresponding terms we get, 2 x - 15 = - x 2 ⇒ x 2 + 2 x - 15 = 0 x 2 + 5 x - 3 x - 15 = 0 x x + 5 - 3 x + 5 = 0 x - 3 x + 5 = 0 x = 3 or - 5 Hence, x = 3 , - 5 . Answer: x is equal to either 3 o r - 5 .

Let A = 5 - 1 6 7 and B = 2 1 3 4 , verify that A ' ' = A .

Given that, A = 5 - 1 6 7 To proof : A ' ' = A Now, A = 5 - 1 6 7 . . . . . . . . . . 1 A ' = 5 6 - 1 7 A ' ' = 5 - 1 6 7 . . . . . . . . . . 2 From equation 1 and 2 , we get A = A ' ' .