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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices2 Marks
Question
Matrix $\text{A}=\begin{bmatrix}0&2\text{b}&-2\\3&1&3\\3\text{a}&3&-1 \end{bmatrix}$ is given to be symmetric, find values of a and b.
✓

Answer

We have
$\text{A}=\begin{bmatrix}0&2\text{b}&-2\\3&1&3\\3\text{a}&3&-1 \end{bmatrix}$
$\text{A}'=\begin{bmatrix}0&3&3\text{a}\\2\text{b}&1&3\\-2&3&-1\end{bmatrix}$
We know thet a matrix is symmetric if A = A'.
Thus,
$\begin{bmatrix}0&2\text{b}&-2\\3&1&3\\3\text{a}&3&-1 \end{bmatrix}=\begin{bmatrix}0&3&3\text{a}\\2\text{b}&1&3\\-2&3&-1\end{bmatrix}$
Now,
2b = 3
$\Rightarrow\text{b}=\frac{3}{2}$
Also,
3a = -2
$\Rightarrow\text{a}=\frac{-2}{3}$
Therefore,
$\text{a}=\frac{-2}{3}$ and $\text{b}=\frac{3}{2}$

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