Full solution

Q. Find the values of

x

and

y

in the following matrix subtraction.

\newline

\begin{array}{l} {\left[\begin{array}{c} 5 \\ x \\ -1 \end{array}\right]-\left[\begin{array}{c} -3 \\ 2 \\ y \end{array}\right]=\left[\begin{array}{c} 8 \\ -5 \\ -6 \end{array}\right]} \\ x=\square \\ y=\square \end{array}

Step $1$ : Subtract first element of first column: Subtract the first element of the first column in the matrices. $\newline$ $5 - (-3) = 5 + 3 = 8$ $\newline$ Check if the result matches the corresponding element in the resulting matrix. $\newline$ $8 = 8$
Step $2$ : Subtract second element of first column to find $x$ : Subtract the second element of the first column in the matrices to find $x$ . $x - 2 = -5$ Solve for $x$ . $x = -5 + 2$ $x = -3$ Check if the subtraction is correct and if $x$ has been correctly solved. $-3 - 2 = -5$
Step $3$ : Subtract third element of first column to find $y$ : Subtract the third element of the first column in the matrices to find $y$ . $-1 - y = -6$ Solve for $y$ . $-y = -6 + 1$ $-y = -5$ Multiply both sides by $-1$ to get $y$ . $y = 5$ Check if the subtraction is correct and if $y$ has been correctly solved. $y$ $0$