Question

If A = `[(1,a,b),(-1,2,c),(0,5,3)]` is a symmetric matrix, then the value of 3a + b + c is ______.

Options

• 2

• 6

• 4

• 0

Answer 1

If A = `[(1,a,b),(-1,2,c),(0,5,3)]` is a symmetric matrix, then the value of 3a + b + c is 2.

Explanation:

A = `[(1,a,b),(-1,2,c),(0,5,3)]`

A^T = `[(1,-1,0),(a,2,5),(b,c,3)]`

A = A^T Symmetric

a = –1, b = 0, c = 5

3a + b + c

= 3 (–1) + 0 + (5)

= –3 + 5 

= 2