Linear Algebra Examples

$a \cdot 2 = 40.3$ , $a \cdot 9 = 252.88$

Step 1

Move $2$ to the left of $a$ .

$2 a = 40.3, a \cdot 9 = 252.88$

Step 2

Move $9$ to the left of $a$ .

$2 a = 40.3, 9 a = 252.88$

Step 3

Write the system of equations in matrix form.

$[\begin{array}{c} 2 & 40.3 \\ 9 & 252.88 \end{array}]$

Step 4

Find the reduced row echelon form.

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

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

$[\begin{array}{c} \frac{2}{2} & \frac{40.3}{2} \\ 9 & 252.88 \end{array}]$

Step 4.1.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & 20.15 \\ 9 & 252.88 \end{array}]$

Step 4.2

Perform the row operation $R_{2} = R_{2} - 9 R_{1}$ to make the entry at $2, 1$ a $0$ .

Tap for more steps...

Step 4.2.1

Perform the row operation $R_{2} = R_{2} - 9 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & 20.15 \\ 9 - 9 \cdot 1 & 252.88 - 9 \cdot 20.15 \end{array}]$

Step 4.2.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & 20.15 \\ 0 & 71.53 \end{array}]$

Step 4.3

Multiply each element of $R_{2}$ by $\frac{1}{71.53}$ to make the entry at $2, 2$ a $1$ .

Tap for more steps...

Step 4.3.1

Multiply each element of $R_{2}$ by $\frac{1}{71.53}$ to make the entry at $2, 2$ a $1$ .

$[\begin{array}{c} 1 & 20.15 \\ \frac{0}{71.53} & \frac{71.53}{71.53} \end{array}]$

Step 4.3.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 & 20.15 \\ 0 & 1 \end{array}]$

Step 4.4

Perform the row operation $R_{1} = R_{1} - 20.15 R_{2}$ to make the entry at $1, 2$ a $0$ .

Tap for more steps...

Step 4.4.1

Perform the row operation $R_{1} = R_{1} - 20.15 R_{2}$ to make the entry at $1, 2$ a $0$ .

$[\begin{array}{c} 1 - 20.15 \cdot 0 & 20.15 - 20.15 \cdot 1 \\ 0 & 1 \end{array}]$

Step 4.4.2

Simplify $R_{1}$ .

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

Step 5

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

$a = 0$

$0 = 1$

Step 6

Since $0 \neq 1$ , there are no solutions.

No solution