Find X and Y, if

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Question

Find X and Y, if $2 [\begin{array}{ll} 1 3 \\ 0 x \end{array}] + [\begin{array}{ll} y 0 \\ 1 2 \end{array}] = [\begin{array}{ll} 5 6 \\ 1 8 \end{array}]$

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$[\begin{array}{cc} 2 & 6 \\ 0 & 2 x \end{array}] + [\begin{array}{ll} y 0 \\ 1 2 \end{array}] = [\begin{array}{ll} 5 6 \\ 1 8 \end{array}]$

$= [\begin{array}{cc} 2 + y & 6 \\ 1 & 2 x + 2 \end{array}] = [\begin{array}{ll} 5 6 \\ 1 8 \end{array}]$

⇒ 2 + y = 5 ∴ y = 5 – 2 ⇒ y = 3

$2 x + 2 = 8 x = \frac{8 - 2}{2} \Rightarrow x = 3$