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Operations of matrix

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Question

Given $A = [\begin{matrix} 1 & 2 & - 3 \\ 5 & 0 & 2 \\ 1 & - 1 & 1 \end{matrix}]$ and $B = [\begin{array}{ccc} 3 & - 1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3 \end{array}]$ then sum of all the elements in the matrix C where A+2C = B is

Easy

Solution

Given, A +2C = B
$2 C = B - A = [\begin{array}{ccc} 3 & - 1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3 \end{array}] - [\begin{array}{ccc} 1 & 2 & - 3 \\ 5 & 0 & 2 \\ 1 & - 1 & 1 \end{array}]$
$\begin{array}{l} = [\begin{array}{ccc} 3 - 1 & - 1 - 2 & 2 + 3 \\ 4 - 5 & 2 - 0 & 5 - 2 \\ 2 - 1 & 0 + 1 & 3 - 1 \end{array}] \\ ∴ 2 C = [\begin{array}{ccc} 2 & - 3 & 5 \\ - 1 & 2 & 3 \\ 1 & 1 & 2 \end{array}] \Rightarrow C = \frac{1}{2} [\begin{array}{rrr} 2 & - 3 & 5 \\ - 1 & 2 & 3 \\ 1 & 1 & 2 \end{array}] \\ = [\begin{array}{ccc} 1 & - \frac{3}{2} & \frac{5}{2} \\ - \frac{1}{2} & 1 & \frac{3}{2} \\ \frac{1}{2} & \frac{1}{2} & 1 \end{array}] \end{array}$

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Similar Questions

Find the sum of all elements in X where $2 X - Y = [\begin{array}{ccc} 3 & - 3 & 0 \\ 3 & 3 & 2 \end{array}], 2 Y + X = [\begin{array}{ccc} 4 & 1 & 5 \\ - 1 & 4 & - 4 \end{array}]$

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