Linear Algebra Examples

$[\begin{array}{c} s - 2 t \\ 3 + 3 s \\ 3 s + t \\ 2 s \end{array}]$

Step 1

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

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Step 1.1

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

$[\begin{array}{c} \frac{s - 2 t}{s - 2 t} \\ 3 + 3 s \\ 3 s + t \\ 2 s \end{array}]$

Step 1.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 \\ 3 + 3 s \\ 3 s + t \\ 2 s \end{array}]$

Step 2

Perform the row operation $R_{2} = R_{2} - (3 + 3 s) R_{1}$ to make the entry at $2, 1$ a $0$ .

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Step 2.1

Perform the row operation $R_{2} = R_{2} - (3 + 3 s) R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 \\ 3 + 3 s - (3 + 3 s) \cdot 1 \\ 3 s + t \\ 2 s \end{array}]$

Step 2.2

Simplify $R_{2}$ .

$[\begin{array}{c} 1 \\ 0 \\ 3 s + t \\ 2 s \end{array}]$

Step 3

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

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Step 3.1

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

$[\begin{array}{c} 1 \\ 0 \\ 3 s + t - (3 s + t) \cdot 1 \\ 2 s \end{array}]$

Step 3.2

Simplify $R_{3}$ .

$[\begin{array}{c} 1 \\ 0 \\ 0 \\ 2 s \end{array}]$

Step 4

Perform the row operation $R_{4} = R_{4} - 2 s R_{1}$ to make the entry at $4, 1$ a $0$ .

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Step 4.1

Perform the row operation $R_{4} = R_{4} - 2 s R_{1}$ to make the entry at $4, 1$ a $0$ .

$[\begin{array}{c} 1 \\ 0 \\ 0 \\ 2 s - 2 s \cdot 1 \end{array}]$

Step 4.2

Simplify $R_{4}$ .

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