Algebra Examples

$[\begin{array}{c} 4 & 2 \\ 0 & 1 \end{array}] + [\begin{array}{c} 5 & 9 \\ 8 & 2 \end{array}] = [\begin{array}{c} 9 & x \\ 8 & 3 \end{array}]$

Step 1

Add the corresponding elements.

$[\begin{array}{c} 4 + 5 & 2 + 9 \\ 0 + 8 & 1 + 2 \end{array}] = [\begin{array}{c} 9 & x \\ 8 & 3 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Add $4$ and $5$ .

$[\begin{array}{c} 9 & 2 + 9 \\ 0 + 8 & 1 + 2 \end{array}] = [\begin{array}{c} 9 & x \\ 8 & 3 \end{array}]$

Step 2.2

Add $2$ and $9$ .

$[\begin{array}{c} 9 & 11 \\ 0 + 8 & 1 + 2 \end{array}] = [\begin{array}{c} 9 & x \\ 8 & 3 \end{array}]$

Step 2.3

Add $0$ and $8$ .

$[\begin{array}{c} 9 & 11 \\ 8 & 1 + 2 \end{array}] = [\begin{array}{c} 9 & x \\ 8 & 3 \end{array}]$

Step 2.4

Add $1$ and $2$ .

$[\begin{array}{c} 9 & 11 \\ 8 & 3 \end{array}] = [\begin{array}{c} 9 & x \\ 8 & 3 \end{array}]$

Step 3

Write as a linear system of equations.

$9 = 9$

$11 = x$

$8 = 8$

$3 = 3$

Step 4

Since $3 = 3$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying $11 = x$ .