Precalculus Examples

[\begin{matrix} 36 \end{matrix}]

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

Step 1

Write as an augmented matrix for

A x = 0

$A x = 0$ .

[\begin{matrix} 3 & 0 6 & 0 \end{matrix}]

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

Step 2

Find the reduced row echelon form.

Tap for more steps...

Step 2.1

Multiply each element of

R_{1}

$R_{1}$ by

\frac{1}{3}

$\frac{1}{3}$ to make the entry at

1, 1

$1, 1$ a

1

$1$ .

Tap for more steps...

Step 2.1.1

Multiply each element of

R_{1}

$R_{1}$ by

\frac{1}{3}

$\frac{1}{3}$ to make the entry at

1, 1

$1, 1$ a

1

$1$ .

[\begin{matrix} \frac{3}{3} & \frac{0}{3} 6 & 0 \end{matrix}]

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

Step 2.1.2

Simplify

R_{1}

$R_{1}$ .

[\begin{matrix} 1 & 0 6 & 0 \end{matrix}]

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

[\begin{matrix} 1 & 0 6 & 0 \end{matrix}]

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

Step 2.2

Perform the row operation

R_{2} = R_{2} - 6 R_{1}

$R_{2} = R_{2} - 6 R_{1}$ to make the entry at

2, 1

$2, 1$ a

0

$0$ .

Tap for more steps...

Step 2.2.1

Perform the row operation

R_{2} = R_{2} - 6 R_{1}

$R_{2} = R_{2} - 6 R_{1}$ to make the entry at

2, 1

$2, 1$ a

0

$0$ .

[\begin{matrix} 1 & 0 6 - 6 \cdot 1 & 0 - 6 \cdot 0 \end{matrix}]

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

Step 2.2.2

Simplify

R_{2}

$R_{2}$ .

[\begin{matrix} 1 & 0 0 & 0 \end{matrix}]

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

[\begin{matrix} 1 & 0 0 & 0 \end{matrix}]

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

[\begin{matrix} 1 & 0 0 & 0 \end{matrix}]

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

Step 3

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

x = 0

$x = 0$

0 = 0

$0 = 0$

Step 4

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

[\begin{matrix} x \end{matrix}] = [\begin{matrix} 0 \end{matrix}]

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

Step 5

Write as a solution set.

{[\begin{matrix} 0 \end{matrix}]}

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

Enter YOUR Problem