Algebra Examples

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

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

Step 1

Add the corresponding elements.

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

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

Step 2

Simplify each element.

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Step 2.1

Subtract

1

$1$ from

1

$1$ .

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

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

Step 2.2

Subtract

1

$1$ from

0

$0$ .

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

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

Step 2.3

Add

0

$0$ and

0

$0$ .

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

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

Step 2.4

Add

1

$1$ and

0

$0$ .

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

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

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

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

Step 3

The determinant of a

2 \times 2

$2 \times 2$ matrix can be found using the formula

| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b

$| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

0 \cdot 1 + 0 \cdot - 1

$0 \cdot 1 + 0 \cdot - 1$

Step 4

Simplify the determinant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply

0

$0$ by

1

$1$ .

0 + 0 \cdot - 1

$0 + 0 \cdot - 1$

Step 4.1.2

Multiply

0

$0$ by

- 1

$- 1$ .

0 + 0

$0 + 0$

0 + 0

$0 + 0$

Step 4.2

Add

0

$0$ and

0

$0$ .

0

$0$

0

$0$

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