Find X, if and .

Engineering

Mathematics

Algebra of Matrices

Question

Find X, if $Y = [\begin{matrix} 3 & 2 \\ 1 & 4 \end{matrix}]$ and $2 X + Y = [\begin{matrix} 1 & 0 \\ - 3 & 2 \end{matrix}]$ .

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$Y = [\begin{array}{cc} 3 & 2 \\ 1 & 4 \end{array}]$

$\Rightarrow 2 X + Y = [\begin{array}{cc} 1 & 0 \\ - 3 & 2 \end{array}]$

$\Rightarrow 2 X = [\begin{array}{cc} 1 & 0 \\ - 3 & 2 \end{array}] - Y$

$\Rightarrow 2 X = [\begin{array}{cc} 1 & 0 \\ - 3 & 2 \end{array}] - [\begin{array}{cc} 3 & 2 \\ 1 & 4 \end{array}]$

$\Rightarrow 2 X = [\begin{array}{cc} 1 - 3 & 0 - 2 \\ - 3 - 1 & 2 - 4 \end{array}]$

$\Rightarrow 2 X = [\begin{array}{cc} - 2 & - 2 \\ - 4 & - 2 \end{array}]$

$\Rightarrow X = \frac{1}{2} [\begin{array}{cc} - 2 & - 2 \\ - 4 & - 2 \end{array}]$

$\Rightarrow X = [\begin{array}{cc} - 1 & - 1 \\ - 2 & - 1 \end{array}]$