Find the value of x and y if: $2 [\begin{matrix} 1 & 3 \\ 0 & x \end{matrix}] + [\begin{matrix} y & 0 \\ 1 & 2 \end{matrix}] = [\begin{matrix} 5 & 6 \\ 1 & 8 \end{matrix}]$

Solution

$2 [\begin{matrix} 1 & 3 \\ 0 & x \end{matrix}] + [\begin{matrix} y & 0 \\ 1 & 2 \end{matrix}] = [\begin{matrix} 5 & 6 \\ 1 & 8 \end{matrix}] [\begin{matrix} 2 & 6 \\ 0 & 2 x \end{matrix}] + [\begin{matrix} y & 0 \\ 1 & 2 \end{matrix}] = [\begin{matrix} 5 & 6 \\ 1 & 8 \end{matrix}] [\begin{matrix} 2 + y & 6 + 0 \\ 0 + 1 & 2 x + 2 \end{matrix}] = [\begin{matrix} 5 & 6 \\ 1 & 8 \end{matrix}] [\begin{matrix} 2 + y & 6 \\ 1 & 2 (x + 1) \end{matrix}] = [\begin{matrix} 5 & 6 \\ 1 & 8 \end{matrix}]$

On comparing the corresponding elements of the matrices on both sides, We get:

2 + y = 5 $\Rightarrow$ y = 3

2 ( x + 1 ) = 8 $\Rightarrow$ x = 3

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Matrices

Find the value of x and y if: $2 [\begin{matrix} 1 & 3 \\ 0 & x \end{matrix}] + [\begin{matrix} y & 0 \\ 1 & 2 \end{matrix}] = [\begin{matrix} 5 & 6 \\ 1 & 8 \end{matrix}]$

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Find the value of x and y if: 2130x + y012 = 5618

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Find the value of x and y if: $2 [\begin{matrix} 1 & 3 \\ 0 & x \end{matrix}] + [\begin{matrix} y & 0 \\ 1 & 2 \end{matrix}] = [\begin{matrix} 5 & 6 \\ 1 & 8 \end{matrix}]$