Question

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Answer 1

Step-by-step explanation:

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Answer 2

Question :

If $\sf{\left[\begin{array}{c c c}1 & 4 \\ -2 & 3\end{array}\right] + 2M = 3\left[\begin{array}{c c c}3 & 2 \\ 0 & -3\end{array}\right]}$, find the value of Matrix M.

Explanation :

Given :

• $\sf{\left[\begin{array}{c c c}1 & 4 \\ -2 & 3\end{array}\right] + 2M = 3\left[\begin{array}{c c c}3 & 2 \\ 0 & -3\end{array}\right]}$

To find :

• The value of matrix M.

Solution :

$:\implies \sf{\left[\begin{array}{c c c}1 & 4 \\ -2 & 3\end{array}\right] + 2M = 3\left[\begin{array}{c c c}3 & 2 \\ 0 & -3\end{array}\right]} \\ \\ \\ :\implies \sf{\left[\begin{array}{c c c}1 & 4 \\ -2 & 3\end{array}\right] + 2M = \left[\begin{array}{c c c}3 \times 3 & 2 \times 3 \\ 0 \times 3 & -3 \times 3\end{array}\right]} \\ \\ \\ :\implies \sf{\left[\begin{array}{c c c}1 & 4 \\ -2 & 3\end{array}\right] + 2M = \left[\begin{array}{c c c}9 & 6 \\ 0 & -9\end{array}\right]} \\ \\ \\ :\implies \sf{2M = \left[\begin{array}{c c c}9 & 6 \\ 0 & -9\end{array}\right] - \left[\begin{array}{c c c}1 & 4 \\ -2 & 3\end{array}\right]} \\ \\ \\ :\implies \sf{2M = \left[\begin{array}{c c c}9 - 1 & 6 - 4 \\ 0 - (-2) & -9 - 3\end{array}\right]} \\ \\ \\ :\implies \sf{2M = \left[\begin{array}{c c c}8 & 2 \\ 2 & -12\end{array}\right]} \\ \\ \\ :\implies \sf{M = \dfrac{1}{2} \times \left[\begin{array}{c c c}8 & 2 \\ 2 & -12\end{array}\right]} \\ \\ \\ :\implies \sf{M = \left[\begin{array}{c c c}8 \times \dfrac{1}{2} & 2 \times \dfrac{1}{2} \\ \\ \\ 2 \times \dfrac{1}{2} & -12 \times \dfrac{1}{2}\end{array}\right]} \\ \\ \\ :\implies \sf{M = \left[\begin{array}{c c c}\not{8} \times \dfrac{1}{\not{2}} & \not{2} \times \dfrac{1}{\not{2}} \\ \\ \not{2} \times \dfrac{1}{\not{2}} & \not{-12} \times \dfrac{1}{\not{2}}\end{array}\right]} \\ \\ \\ :\implies \sf{M = \left[\begin{array}{c c c}4 & 1 \\ 1 & -6\end{array}\right]}$

$\boxed{\therefore \sf{M = \left[\begin{array}{c c c}4 & 1 \\ 1 & -6\end{array}\right]}}$

Hence the value of matrix M is $\sf{\left[\begin{array}{c c c}4 & 1 \\ 1 & -6\end{array}\right]}$