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Problem 2: Solve the matrix equation for "x" and "y" 8 -X 2 13 4 1- [ 3 -9 10 -4y 5 6 [ 0 16

Problem 2: Solve the matrix equation for "x" and "y" 8 -X 2 13 4 1- [ 3 -9 10 -4y-example-1
User Jim Biard
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1 Answer

3 votes

Solve the operation of the matrix


\begin{gathered} 2\begin{bmatrix}{8} & {-x} & {} \\ {5} & {6} & {} \\ & {} & {}\end{bmatrix}{}-\begin{bmatrix}{3} & {-9} & {} \\ {10} & {-4y} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{13} & {4} & {} \\ {0} & {16} & {} \\ {} & {} & {}\end{bmatrix} \\ \begin{bmatrix}{16} & {-2x} & {} \\ {10} & {12} & {} \\ {} & & {}\end{bmatrix}-\begin{bmatrix}{3} & {-9} & {} \\ {10} & {-4y} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{13} & {4} & {} \\ {0} & {16} & {} \\ {} & {} & {}\end{bmatrix} \\ \begin{bmatrix}{13} & {-2x+9} & {} \\ {0} & {12+4y} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{13} & {4} & {} \\ {0} & {16} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}

From this result we know that


\begin{gathered} -2x+9=4 \\ 12+4y=16 \end{gathered}

Now clear x and y from the equations


\begin{gathered} -2x+9=4 \\ -2x=-5 \\ x=-(5)/(-2) \\ x=(5)/(2) \end{gathered}
\begin{gathered} 12+4y=16 \\ 4y=4 \\ y=(4)/(4) \\ y=1 \end{gathered}

x is 5/2 and y is 1

User Eqbal Sohrabi
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