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Last updated date: 01st Dec 2023
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# If we have the summation of matrices $2\left[ \begin{matrix} 3 & 4 \\ 5 & x \\\end{matrix} \right]+\left[ \begin{matrix} 1 & y \\ 0 & 1 \\\end{matrix} \right]=\left[ \begin{matrix} 7 & 0 \\ 10 & 5 \\\end{matrix} \right]$ find the values of x and y.

According to our question it is asked of us if, $2\left[ \begin{matrix} 3 & 4 \\ 5 & x \\ \end{matrix} \right]+\left[ \begin{matrix} 1 & y \\ 0 & 1 \\ \end{matrix} \right]=\left[ \begin{matrix} 7 & 0 \\ 10 & 5 \\ \end{matrix} \right]$ , then find the values of x and y. So, as we know that the question is given in a form of matrices and if we want to calculate the value of x and y, then we have to solve this as a single -single matrix form on both sides. So, if we add both the matrices to each other and before that we will do all the calculations of multiplication and division in that and then we add to the solved matrices and will get a final matrix in LHS. And also s single matrix is available in RHS. So, if we compare both the matrices with each other, then these both will provide the answer. For that, we will write it as:
\begin{align} & \Rightarrow 2\left[ \begin{matrix} 3 & 4 \\ 5 & x \\ \end{matrix} \right]+\left[ \begin{matrix} 1 & y \\ 0 & 1 \\ \end{matrix} \right]=\left[ \begin{matrix} 6 & 8 \\ 10 & 2x \\ \end{matrix} \right]+\left[ \begin{matrix} 1 & y \\ 0 & 1 \\ \end{matrix} \right] \\ & \Rightarrow \left[ \begin{matrix} 6+1 & 8+y \\ 10+0 & 2x+1 \\ \end{matrix} \right]=\left[ \begin{matrix} 7 & 8+y \\ 10 & 2x+1 \\ \end{matrix} \right] \\ & \Rightarrow \left[ \begin{matrix} 7 & 8+y \\ 10 & 2x+1 \\ \end{matrix} \right]=\left[ \begin{matrix} 7 & 0 \\ 10 & 5 \\ \end{matrix} \right] \\ \end{align}
\begin{align} & 8+y=0 \\ &\Rightarrow y=-8 \\ & 2x+1=5 \\ &\Rightarrow 2x=4 \\ &\Rightarrow x=2 \\ \end{align}