Algebra Examples

$2 [\begin{array}{c} - a \\ b \end{array}] - [\begin{array}{c} - 2 a \\ 2 b \\ c \end{array}] = [\begin{array}{c} 4 \\ - 1 \\ - 4 \end{array}]$

Step 1

Simplify each term.

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Step 1.1

Multiply $2$ by each element of the matrix.

$[\begin{array}{c} 2 (- a) \\ 2 b \end{array}] - [\begin{array}{c} - 2 a \\ 2 b \\ c \end{array}] = [\begin{array}{c} 4 \\ - 1 \\ - 4 \end{array}]$

Step 1.2

Multiply $- 1$ by $2$ .

$[\begin{array}{c} - 2 a \\ 2 b \end{array}] - [\begin{array}{c} - 2 a \\ 2 b \\ c \end{array}] = [\begin{array}{c} 4 \\ - 1 \\ - 4 \end{array}]$

Step 2

The matrix equation can be written as a set of equations.

$- 2 a - 2 a = 4$

$2 b + 2 b = - 1$

Step 3

Divide each term in $- 4 a = 4$ by $- 4$ and simplify.

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Step 3.1

Divide each term in $- 4 a = 4$ by $- 4$ .

$\frac{- 4 a}{- 4} = \frac{4}{- 4}$

$4 b = - 1$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 4 a}{- 4} = \frac{4}{- 4}$

$4 b = - 1$

Step 3.2.1.2

Divide $a$ by $1$ .

$a = \frac{4}{- 4}$

$4 b = - 1$

$a = \frac{4}{- 4}$

$4 b = - 1$

$a = \frac{4}{- 4}$

$4 b = - 1$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $4$ by $- 4$ .

$a = - 1$

$4 b = - 1$

$a = - 1$

$4 b = - 1$

$a = - 1$

$4 b = - 1$

Step 4

Divide each term in $4 b = - 1$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 b = - 1$ by $4$ .

$\frac{4 b}{4} = \frac{- 1}{4}$

$a = - 1$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 b}{4} = \frac{- 1}{4}$

$a = - 1$

Step 4.2.1.2

Divide $b$ by $1$ .

$b = \frac{- 1}{4}$

$a = - 1$

$b = \frac{- 1}{4}$

$a = - 1$

$b = \frac{- 1}{4}$

$a = - 1$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$b = - \frac{1}{4}$

$a = - 1$

$b = - \frac{1}{4}$

$a = - 1$

$b = - \frac{1}{4}$

$a = - 1$

Step 5

List all of the solutions.

$b = - \frac{1}{4}, a = - 1$