Linear Algebra Examples

$u = [\begin{array}{c} 2 i & - 3 j & k \end{array}]$

Step 1

Find the reduced row echelon form.

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Step 1.1

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

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Step 1.1.1

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

$[\begin{array}{c} \frac{2 i}{2 i} & \frac{- 3 j}{2 i} & \frac{k}{2 i} \end{array}]$

Step 1.1.2

Simplify $R_{1}$ .

$[\begin{array}{c} 1 & \frac{3 j i}{2} & - \frac{k i}{2} \end{array}]$

Step 2

The pivot positions are the locations with the leading $1$ in each row. The pivot columns are the columns that have a pivot position.

Pivot Positions: $u_{11}$

Pivot Columns: $1$