Finite Math Examples

[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] - 2 [\begin{array}{c} - 9 & 4 & 3 \\ 9 & 10 & 4 \\ - 9 & y & 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] - 2 [\begin{array}{c} - 9 & 4 & 3 \\ 9 & 10 & 4 \\ - 9 & y & 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Step 1

Simplify each term.

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Step 1.1

Multiply

- 2

$- 2$ by each element of the matrix.

[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} - 2 \cdot - 9 & - 2 \cdot 4 & - 2 \cdot 3 \\ - 2 \cdot 9 & - 2 \cdot 10 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} - 2 \cdot - 9 & - 2 \cdot 4 & - 2 \cdot 3 \\ - 2 \cdot 9 & - 2 \cdot 10 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Step 1.2

Simplify each element in the matrix.

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Step 1.2.1

Multiply

- 2

$- 2$ by

- 9

$- 9$ .

[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 2 \cdot 4 & - 2 \cdot 3 \\ - 2 \cdot 9 & - 2 \cdot 10 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 2 \cdot 4 & - 2 \cdot 3 \\ - 2 \cdot 9 & - 2 \cdot 10 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Step 1.2.2

Multiply

- 2

$- 2$ by

4

$4$ .

[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 2 \cdot 3 \\ - 2 \cdot 9 & - 2 \cdot 10 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 2 \cdot 3 \\ - 2 \cdot 9 & - 2 \cdot 10 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Step 1.2.3

Multiply

- 2

$- 2$ by

3

$3$ .

[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 2 \cdot 9 & - 2 \cdot 10 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 2 \cdot 9 & - 2 \cdot 10 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Step 1.2.4

Multiply

- 2

$- 2$ by

9

$9$ .

[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 2 \cdot 10 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 2 \cdot 10 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Step 1.2.5

Multiply

- 2

$- 2$ by

10

$10$ .

[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 20 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 20 & - 2 \cdot 4 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Step 1.2.6

Multiply

- 2

$- 2$ by

4

$4$ .

[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 20 & - 8 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 20 & - 8 \\ - 2 \cdot - 9 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Step 1.2.7

Multiply

- 2

$- 2$ by

- 9

$- 9$ .

[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 20 & - 8 \\ 18 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 20 & - 8 \\ 18 & - 2 y & - 2 \cdot 10 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Step 1.2.8

Multiply

- 2

$- 2$ by

10

$10$ .

[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 20 & - 8 \\ 18 & - 2 y & - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 20 & - 8 \\ 18 & - 2 y & - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 20 & - 8 \\ 18 & - 2 y & - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

[\begin{array}{c} x & - 42 & - 14 \\ - 27 & z & 18 \\ 10 & 8 & 65 \end{array}] + [\begin{array}{c} 18 & - 8 & - 6 \\ - 18 & - 20 & - 8 \\ 18 & - 2 y & - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

Step 2

Add the corresponding elements.

[\begin{array}{c} x + 18 & - 42 - 8 & - 14 - 6 \\ - 27 - 18 & z - 20 & 18 - 8 \\ 10 + 18 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x + 18 & - 42 - 8 & - 14 - 6 \\ - 27 - 18 & z - 20 & 18 - 8 \\ 10 + 18 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Step 3

Simplify each element.

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Step 3.1

Subtract

8

$8$ from

- 42

$- 42$ .

[\begin{array}{c} x + 18 & - 50 & - 14 - 6 \\ - 27 - 18 & z - 20 & 18 - 8 \\ 10 + 18 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 14 - 6 \\ - 27 - 18 & z - 20 & 18 - 8 \\ 10 + 18 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Step 3.2

Subtract

6

$6$ from

- 14

$- 14$ .

[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 27 - 18 & z - 20 & 18 - 8 \\ 10 + 18 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 27 - 18 & z - 20 & 18 - 8 \\ 10 + 18 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Step 3.3

Subtract

18

$18$ from

- 27

$- 27$ .

[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 18 - 8 \\ 10 + 18 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 18 - 8 \\ 10 + 18 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Step 3.4

Subtract

8

$8$ from

18

$18$ .

[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 10 + 18 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 10 + 18 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Step 3.5

Add

10

$10$ and

18

$18$ .

[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 65 - 20 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Step 3.6

Subtract

20

$20$ from

65

$65$ .

[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = - 5 [\begin{array}{c} 2 & 10 & 4 \\ 9 & 8 & - 2 \\ w & - 4 & - 9 \end{array}]$

Step 4

Multiply

- 5

$- 5$ by each element of the matrix.

[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 5 \cdot 2 & - 5 \cdot 10 & - 5 \cdot 4 \\ - 5 \cdot 9 & - 5 \cdot 8 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 5 \cdot 2 & - 5 \cdot 10 & - 5 \cdot 4 \\ - 5 \cdot 9 & - 5 \cdot 8 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]$

Step 5

Simplify each element in the matrix.

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Step 5.1

Multiply

- 5

$- 5$ by

2

$2$ .

[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 5 \cdot 10 & - 5 \cdot 4 \\ - 5 \cdot 9 & - 5 \cdot 8 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 5 \cdot 10 & - 5 \cdot 4 \\ - 5 \cdot 9 & - 5 \cdot 8 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]$

Step 5.2

Multiply

- 5

$- 5$ by

10

$10$ .

[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 5 \cdot 4 \\ - 5 \cdot 9 & - 5 \cdot 8 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 5 \cdot 4 \\ - 5 \cdot 9 & - 5 \cdot 8 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]$

Step 5.3

Multiply

- 5

$- 5$ by

4

$4$ .

[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 5 \cdot 9 & - 5 \cdot 8 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 5 \cdot 9 & - 5 \cdot 8 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]$

Step 5.4

Multiply

- 5

$- 5$ by

9

$9$ .

[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 5 \cdot 8 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 5 \cdot 8 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]$

Step 5.5

Multiply

- 5

$- 5$ by

8

$8$ .

[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 40 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 40 & - 5 \cdot - 2 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]$

Step 5.6

Multiply

- 5

$- 5$ by

- 2

$- 2$ .

[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 40 & 10 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 40 & 10 \\ - 5 w & - 5 \cdot - 4 & - 5 \cdot - 9 \end{array}]$

Step 5.7

Multiply

- 5

$- 5$ by

- 4

$- 4$ .

[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 40 & 10 \\ - 5 w & 20 & - 5 \cdot - 9 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 40 & 10 \\ - 5 w & 20 & - 5 \cdot - 9 \end{array}]$

Step 5.8

Multiply

- 5

$- 5$ by

- 9

$- 9$ .

[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 40 & 10 \\ - 5 w & 20 & 45 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 40 & 10 \\ - 5 w & 20 & 45 \end{array}]$

[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 40 & 10 \\ - 5 w & 20 & 45 \end{array}]

$[\begin{array}{c} x + 18 & - 50 & - 20 \\ - 45 & z - 20 & 10 \\ 28 & 8 - 2 y & 45 \end{array}] = [\begin{array}{c} - 10 & - 50 & - 20 \\ - 45 & - 40 & 10 \\ - 5 w & 20 & 45 \end{array}]$

Step 6

Write as a linear system of equations.

x + 18 = - 10

$x + 18 = - 10$

- 50 = - 50

$- 50 = - 50$

- 20 = - 20

$- 20 = - 20$

- 45 = - 45

$- 45 = - 45$

z - 20 = - 40

$z - 20 = - 40$

10 = 10

$10 = 10$

28 = - 5 w

$28 = - 5 w$

8 - 2 y = 20

$8 - 2 y = 20$

45 = 45

$45 = 45$

Step 7

Since

45 = 45

$45 = 45$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying the system.