Matrix \(A = \begin{bmatrix} 0 & 2b & -2\\[0.3em] 3 & 1& 3 \\[0.3em]

1.	Matrix \(A = \begin{bmatrix} 0 & 2b & -2\\[0.3em] 3 & 1& 3 \\[0.3em] 3a&3 & -1 \end{bmatrix}\)is given to be symmetric, find values of a and b.
Answer» We have, \(A = \begin{bmatrix} 0 & 2b & -2\\[0.3em] 3 & 1& 3 \\[0.3em] 3a&3 & -1 \end{bmatrix}\) ∵ A is symmetric matrix. ⇒ A^T = A ⇒ \( \begin{bmatrix} 0 & 3 & 3a\\[0.3em] 2b& 1& 3 \\[0.3em] -2&3 & -1 \end{bmatrix}\) = \( \begin{bmatrix} 0 & 2b & -2\\[0.3em] 3& 1& 3 \\[0.3em] 3a&3 & -1 \end{bmatrix}\) Equating both sides, we get 2b = 3 and 3a = - 2 ⇒ b = \(\frac{3}{2}\) and a = \(-\frac{2}{3}\)

Matrix \(A = \begin{bmatrix} 0 & 2b & -2\\[0.3em] 3 & 1& 3 \\[0.3em] 3a&3 & -1 \end{bmatrix}\)is given to be symmetric, find values of a and b.

Answer»

We have,

\(A = \begin{bmatrix} 0 & 2b & -2\\[0.3em] 3 & 1& 3 \\[0.3em] 3a&3 & -1 \end{bmatrix}\)

∵ A is symmetric matrix.

⇒ A^T = A

⇒ \( \begin{bmatrix} 0 & 3 & 3a\\[0.3em] 2b& 1& 3 \\[0.3em] -2&3 & -1 \end{bmatrix}\)

= \( \begin{bmatrix} 0 & 2b & -2\\[0.3em] 3& 1& 3 \\[0.3em] 3a&3 & -1 \end{bmatrix}\)

Equating both sides, we get

2b = 3 and 3a = - 2

⇒ b = \(\frac{3}{2}\) and a = \(-\frac{2}{3}\)