Question

Write the matrix equation as a system of linear equations without matrices. [Start 3 By 3 Matrix 1st Row 1st Column 1 2nd Column negative 2 3rd Column negative 4 2nd Row 1st Column 5 2nd Column negative 4 3rd Column 7 3rd Row 1st Column negative 7 2nd Column 5 3rd Column 2 EndMatrix ][Start 3 By 1 Matrix 1st Row 1st Column x 2nd Row 1st Column y 3rd Row 1st Column z EndMatrix ]equals [Start 3 By 1 Matrix 1st Row 1st Column 8 2nd Row 1st Column 5 3rd Row 1st Column negative 3 EndMatrix ]

Answer 1

Answer:

$x-2y-4z=8\\5x-4y+7z=5\\-7x+5y+2z=-3$

Step-by-step explanation:

Given the matrix equation below:

$\left(\begin{array}{ccc}1&-2&-4\\5&-4&7\\-7&5&2\end{array}\right)\left(\begin{array}{ccc}x\\y\\z\end{array}\right) =\left(\begin{array}{ccc}8\\5\\-3\end{array}\right)$

We are required to write the matrix equation as a system of linear equations without matrices.

$\left(\begin{array}{ccc}1&-2&-4\\&&\\&&\end{array}\right)\left(\begin{array}{ccc}x\\y\\z\end{array}\right) =\left(\begin{array}{ccc}8\\&\\&\end{array}\right) is equivalent to: x-2y-4z=8$

$\left(\begin{array}{ccc}\\5&-4&7\\&&\end{array}\right)\left(\begin{array}{ccc}x\\y\\z\end{array}\right) =\left(\begin{array}{ccc}&\\5\\&\end{array}\right) is equivalent to: 5x-4y+7z=5$

$\left(\begin{array}{ccc}&\\&\\-7&5&2\end{array}\right)\left(\begin{array}{ccc}x\\y\\z\end{array}\right) =\left(\begin{array}{ccc}&\\&\\-3\end{array}\right) is equivalent to: -7x+5y+2z=-3$

Therefore, we have the system of equations:

$x-2y-4z=8\\5x-4y+7z=5\\-7x+5y+2z=-3$