Linear Algebra Examples

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

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

Step 1

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

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Step 1.1

Subtract

[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]

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

x = [\begin{array}{c} 2 & - 2 \\ 9 & - 9 \end{array}] - [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]

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

x = [\begin{array}{c} 2 & - 2 \\ 9 & - 9 \end{array}] - [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]

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

Step 2

Simplify the right side.

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Step 2.1

Subtract the corresponding elements.

x = [\begin{array}{c} 2 - 1 & - 2 - 0 \\ 9 - 0 & - 9 - 1 \end{array}]

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

Step 2.2

Simplify each element.

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Step 2.2.1

Subtract

1

$1$ from

2

$2$ .

x = [\begin{array}{c} 1 & - 2 - 0 \\ 9 - 0 & - 9 - 1 \end{array}]

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

Step 2.2.2

Subtract

0

$0$ from

- 2

$- 2$ .

x = [\begin{array}{c} 1 & - 2 \\ 9 - 0 & - 9 - 1 \end{array}]

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

Step 2.2.3

Subtract

0

$0$ from

9

$9$ .

x = [\begin{array}{c} 1 & - 2 \\ 9 & - 9 - 1 \end{array}]

$x = [\begin{array}{c} 1 & - 2 \\ 9 & - 9 - 1 \end{array}]$

Step 2.2.4

Subtract

1

$1$ from

- 9

$- 9$ .

x = [\begin{array}{c} 1 & - 2 \\ 9 & - 10 \end{array}]

$x = [\begin{array}{c} 1 & - 2 \\ 9 & - 10 \end{array}]$

x = [\begin{array}{c} 1 & - 2 \\ 9 & - 10 \end{array}]

$x = [\begin{array}{c} 1 & - 2 \\ 9 & - 10 \end{array}]$

x = [\begin{array}{c} 1 & - 2 \\ 9 & - 10 \end{array}]

$x = [\begin{array}{c} 1 & - 2 \\ 9 & - 10 \end{array}]$

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