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Question
Matrix A = \[\begin{bmatrix}0 & 2b & - 2 \\ 3 & 1 & 3 \\ 3a & 3 & - 1\end{bmatrix}\] is given to be symmetric, find values of a and b.
Solution
We have
\[A = \begin{bmatrix}0 & 2b & - 2 \\ 3 & 1 & 3 \\ 3a & 3 & - 1\end{bmatrix}\]
\[A' = \begin{bmatrix}0 & 3 & 3a \\ 2b & 1 & 3 \\ - 2 & 3 & - 1\end{bmatrix}\]
We know that a matrix is symmetric if A = A'.
Thus ,
Now,
\[Also, \]
\[3a = - 2\]
\[ \Rightarrow a = \frac{- 2}{3}\]
\[Therefore, \]
`a =(-2)/3 and b = 3/2`
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