Question

Solve the following matrix system: The explanation how you did it would help! Thanks in advance!

Answer 1

Answer:

See below

Step-by-step explanation:

$X - Y = \begin{pmatrix} 1 & 2 & 7 \\ - 1 & 3 & 5 \\ 3 & 1 & 7 \end{pmatrix} \\\\ X + Y = \begin{pmatrix} 1 & 0 & 1 \\ 1 & 1 & 3 \\ - 1 & 3 & 3 \end{pmatrix} \\ adding \: both \: the \: matrices \\ \\ X - Y + X + Y \\ = \begin{pmatrix} 1 & 2 & 7 \\ - 1 & 3 & 5 \\ 3 & 1 & 7 \end{pmatrix} + \begin{pmatrix} 1 & 0 & 1 \\ 1 & 1 & 3 \\ - 1 & 3 & 3 \end{pmatrix} \\\\ 2X= \begin{pmatrix} 1 + 1 & 2 + 0 & 7 + 1 \\ - 1 + 1 & 3 + 1 & 5 + 3\\ 3 - 1 & 1 + 3 & 7 + 3 \end{pmatrix} \\ \\ 2X= \begin{pmatrix} 2 & 2 & 8 \\ 0 & 4 & 8\\ 2 & 4 & 10 \end{pmatrix} \\ \\ X= \frac{1}{2} \begin{pmatrix} 2 & 2 & 8 \\ 0 & 4 & 8\\ 2 & 4 & 10 \end{pmatrix}\\ \\ X= \huge\begin{pmatrix} \frac{2}{2} & \frac{2}{2} & \frac{8}{2} \\ \\ \frac{0}{2} & \frac{4}{2} & \frac{8}{2}\\ \\ \frac{2}{2} & \frac{4}{2} & \frac{10}{2} \end{pmatrix} \\ \\ \huge \red{X= \begin{pmatrix} 1 & 1 & 4\\ \\ 0 & 2 & 4\\ \\ 1 & 2& 5 \end{pmatrix}} \\ \\ subtracting \: the \: value \: of \: x \: from \: matrix \: (2) \\ \\ X + Y - X \\ = \begin{pmatrix} 1 & 0 & 1 \\ 1 & 1 & 3 \\ - 1 & 3 & 3 \end{pmatrix} - \begin{pmatrix} 1 & 1 & 4 \\ 0 & 2 & 4\\ 1 & 2& 5 \end{pmatrix} \\ \\ Y = \begin{pmatrix} 1 - 1 & 0 - 1 & 1 - 4 \\ 1 - 0& 1 - 2 & 3 - 4 \\ - 1 - 1 & 3 - 2 & 3 - 5 \end{pmatrix} \\ \\ \huge \purple{Y = \begin{pmatrix} 0 & - 1 & - 3 \\ 1 & - 1 & - 1 \\ - 2 & 1 & - 2 \end{pmatrix}}$