Finite Math Examples

$[\begin{array}{c} 2 & - 3 & 2 & 2.2 \\ 1 & 1 & - 1 & 0 \\ 3 & 2 & - 4 & - 5.5 \end{array}]$

Step 1

Multiply each element of $R_{1}$ by $\frac{1}{2}$ to make the entry at $1, 1$ a $1$ .

Tap for more steps...

Step 1.1

Multiply each element of $R_{1}$ by $\frac{1}{2}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{2}{2} & \frac{- 3}{2} & \frac{2}{2} & \frac{2.2}{2} \\ 1 & 1 & - 1 & 0 \\ 3 & 2 & - 4 & - 5.5 \end{array}]$

Step 1.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & - \frac{3}{2} & 1 & 1.1 \\ 1 & 1 & - 1 & 0 \\ 3 & 2 & - 4 & - 5.5 \end{array}]$

Step 2

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

Tap for more steps...

Step 2.1

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

$[\begin{array}{c} 1 & - \frac{3}{2} & 1 & 1.1 \\ 1 - 1 & 1 + \frac{3}{2} & - 1 - 1 & 0 - 1.1 \\ 3 & 2 & - 4 & - 5.5 \end{array}]$

Step 2.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & - \frac{3}{2} & 1 & 1.1 \\ 0 & \frac{5}{2} & - 2 & - 1.1 \\ 3 & 2 & - 4 & - 5.5 \end{array}]$

Step 3

Perform the row operation $R_{3} = R_{3} - 3 R_{1}$ to make the entry at $3, 1$ a $0$ .

Tap for more steps...

Step 3.1

Perform the row operation $R_{3} = R_{3} - 3 R_{1}$ to make the entry at $3, 1$ a $0$ .

$[\begin{array}{c} 1 & - \frac{3}{2} & 1 & 1.1 \\ 0 & \frac{5}{2} & - 2 & - 1.1 \\ 3 - 3 \cdot 1 & 2 - 3 (- \frac{3}{2}) & - 4 - 3 \cdot 1 & - 5.5 - 3 \cdot 1.1 \end{array}]$

Step 3.2

Simplify $R_{3}$ .

$[\begin{array}{c} 1 & - \frac{3}{2} & 1 & 1.1 \\ 0 & \frac{5}{2} & - 2 & - 1.1 \\ 0 & \frac{13}{2} & - 7 & - 8.8 \end{array}]$

Step 4

Multiply each element of $R_{2}$ by $\frac{2}{5}$ to make the entry at $2, 2$ a $1$ .

Tap for more steps...

Step 4.1

Multiply each element of $R_{2}$ by $\frac{2}{5}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & - \frac{3}{2} & 1 & 1.1 \\ \frac{2}{5} \cdot 0 & \frac{2}{5} \cdot \frac{5}{2} & \frac{2}{5} \cdot - 2 & \frac{2}{5} \cdot - 1.1 \\ 0 & \frac{13}{2} & - 7 & - 8.8 \end{array}]$

Step 4.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & - \frac{3}{2} & 1 & 1.1 \\ 0 & 1 & - \frac{4}{5} & - 0.44 \\ 0 & \frac{13}{2} & - 7 & - 8.8 \end{array}]$

Step 5

Perform the row operation $R_{3} = R_{3} - \frac{13}{2} R_{2}$ to make the entry at $3, 2$ a $0$ .

Tap for more steps...

Step 5.1

Perform the row operation $R_{3} = R_{3} - \frac{13}{2} R_{2}$ to make the entry at $3, 2$ a $0$ .

$[\begin{array}{c} 1 & - \frac{3}{2} & 1 & 1.1 \\ 0 & 1 & - \frac{4}{5} & - 0.44 \\ 0 - \frac{13}{2} \cdot 0 & \frac{13}{2} - \frac{13}{2} \cdot 1 & - 7 - \frac{13}{2} (- \frac{4}{5}) & - 8.8 - \frac{13}{2} \cdot - 0.44 \end{array}]$

Step 5.2

Simplify $R_{3}$ .

$[\begin{array}{c} 1 & - \frac{3}{2} & 1 & 1.1 \\ 0 & 1 & - \frac{4}{5} & - 0.44 \\ 0 & 0 & - \frac{9}{5} & - 5.94 \end{array}]$

Step 6

Multiply each element of $R_{3}$ by $- \frac{5}{9}$ to make the entry at $3, 3$ a $1$ .

Tap for more steps...

Step 6.1

Multiply each element of $R_{3}$ by $- \frac{5}{9}$ to make the entry at $3, 3$ a $1$ .

$[\begin{array}{c} 1 & - \frac{3}{2} & 1 & 1.1 \\ 0 & 1 & - \frac{4}{5} & - 0.44 \\ - \frac{5}{9} \cdot 0 & - \frac{5}{9} \cdot 0 & - \frac{5}{9} (- \frac{9}{5}) & - \frac{5}{9} \cdot - 5.94 \end{array}]$

Step 6.2

Simplify $R_{3}$ .

$[\begin{array}{c} 1 & - \frac{3}{2} & 1 & 1.1 \\ 0 & 1 & - \frac{4}{5} & - 0.44 \\ 0 & 0 & 1 & 3.3 \end{array}]$

Step 7

Perform the row operation $R_{2} = R_{2} + \frac{4}{5} R_{3}$ to make the entry at $2, 3$ a $0$ .

Tap for more steps...

Step 7.1

Perform the row operation $R_{2} = R_{2} + \frac{4}{5} R_{3}$ to make the entry at $2, 3$ a $0$ .

$[\begin{array}{c} 1 & - \frac{3}{2} & 1 & 1.1 \\ 0 + \frac{4}{5} \cdot 0 & 1 + \frac{4}{5} \cdot 0 & - \frac{4}{5} + \frac{4}{5} \cdot 1 & - 0.44 + \frac{4}{5} \cdot 3.3 \\ 0 & 0 & 1 & 3.3 \end{array}]$

Step 7.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & - \frac{3}{2} & 1 & 1.1 \\ 0 & 1 & 0 & 2.2 \\ 0 & 0 & 1 & 3.3 \end{array}]$

Step 8

Perform the row operation $R_{1} = R_{1} - R_{3}$ to make the entry at $1, 3$ a $0$ .

Tap for more steps...

Step 8.1

Perform the row operation $R_{1} = R_{1} - R_{3}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 - 0 & - \frac{3}{2} - 0 & 1 - 1 & 1.1 - 3.3 \\ 0 & 1 & 0 & 2.2 \\ 0 & 0 & 1 & 3.3 \end{array}]$

Step 8.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & - \frac{3}{2} & 0 & - 2.2 \\ 0 & 1 & 0 & 2.2 \\ 0 & 0 & 1 & 3.3 \end{array}]$

Step 9

Perform the row operation $R_{1} = R_{1} + \frac{3}{2} R_{2}$ to make the entry at $1, 2$ a $0$ .

Tap for more steps...

Step 9.1

Perform the row operation $R_{1} = R_{1} + \frac{3}{2} R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 + \frac{3}{2} \cdot 0 & - \frac{3}{2} + \frac{3}{2} \cdot 1 & 0 + \frac{3}{2} \cdot 0 & - 2.2 + \frac{3}{2} \cdot 2.2 \\ 0 & 1 & 0 & 2.2 \\ 0 & 0 & 1 & 3.3 \end{array}]$

Step 9.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 0 & 0 & 1.1 \\ 0 & 1 & 0 & 2.2 \\ 0 & 0 & 1 & 3.3 \end{array}]$