Find X, if and .

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Question

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

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

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

$x = {[\begin{array}{cc} - 1 & - 1 \\ - 2 & - 1 \end{array}]}_{2 \times 2}$