Question

Write the matrix equation as a system of linear equations without matrices.

Answer 1

The system of equations is 5x - y - 5 = -7, -6x + 6y + 3z = 8 and -6x - 8y - 2z = 2

How to determine the system of equations?

The matrix is given as:

$\left[\begin{array}{ccc}5&-1&-5\\-6&6&3\\-6&-8&-9\end{array}\right] \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}-7&8&2\end{array}\right]$

Next, we multiply the matrices

$\left[\begin{array}{c}5x - y - 5&-6x + 6y + 3z&-6x -8y -2z\end{array}\right] = \left[\begin{array}{c}-7&8&2\end{array}\right]$

By comparing the position of the cells, we have

5x - y - 5 = -7

-6x + 6y + 3z = 8

-6x - 8y - 2z = 2

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Answer 2

The system of equations is 5x - y - 5z = -7, -6x + 6y + 3z = 8, and -6x -8y -2z = 2 which is represented by the matrix in the provided picture.

What is the matrix?

It is defined as the group of numerical data, functions, and complex numbers in a specific way such that the representation array looks like a square, rectangle shape.

We have given matrices in the picture that represents the system of the equation.

$\rm \left[\begin{array}{ccc}5&-1&-5\\-6&6&3\\-6&-8&-2\end{array}\right] \rm \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}-7\\8\\2\end{array}\right]$

After the multiplication of two matrices:

$\rm \left[\begin{array}{ccc}5x-y-5z\\-6x+6y+3z\\-6x-8y-2z\end{array}\right] = \left[\begin{array}{ccc}-7\\8\\2\end{array}\right]$

On comparing:

5x - y - 5z = -7

-6x + 6y + 3z = 8

-6x -8y -2z = 2

Thus, the system of equations are 5x - y - 5z = -7, -6x + 6y + 3z = 8, and -6x -8y -2z = 2 which is represented by the matrix in the provided picture.

Learn more about the matrix here:

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