Examples

$[\begin{array}{c} 3 \\ 6 \end{array}]$

Step 1

Write as an augmented matrix for $A x = 0$ .

$[\begin{array}{c} 3 & 0 \\ 6 & 0 \end{array}]$

Step 2

Find the reduced row echelon form.

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Step 2.1

Multiply each element of $R_{1}$ by $\frac{1}{3}$ to make the entry at $1, 1$ a $1$ .

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Step 2.1.1

Multiply each element of $R_{1}$ by $\frac{1}{3}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{3}{3} & \frac{0}{3} \\ 6 & 0 \end{array}]$

Step 2.1.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 0 \\ 6 & 0 \end{array}]$

Step 2.2

Perform the row operation $R_{2} = R_{2} - 6 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Step 2.2.1

Perform the row operation $R_{2} = R_{2} - 6 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 0 \\ 6 - 6 \cdot 1 & 0 - 6 \cdot 0 \end{array}]$

Step 2.2.2

Simplify $R_{2}$ .

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

Step 3

Use the result matrix to declare the final solution to the system of equations.

$x = 0$

$0 = 0$

Step 4

Write a solution vector by solving in terms of the free variables in each row.

$[\begin{array}{c} x \end{array}] = [\begin{array}{c} 0 \end{array}]$

Step 5

Write as a solution set.

${[\begin{array}{c} 0 \end{array}]}$

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