Linear Algebra Examples

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

Step 1

Move all terms not containing a variable to the right side.

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Step 1.1

Add $[\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}]$ to both sides of the equation.

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

Step 2

Simplify the right side.

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Step 2.1

Add the corresponding elements.

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

Step 2.2

Simplify each element.

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Step 2.2.1

Add $2$ and $1$ .

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

Step 2.2.2

Subtract $1$ from $2$ .

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

Step 2.2.3

Add $2$ and $0$ .

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

Step 2.2.4

Add $8$ and $0$ .

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

Step 2.2.5

Add $3$ and $1$ .

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

Step 2.2.6

Add $4$ and $1$ .

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