Linear Algebra Examples

$X = [\begin{array}{c} 1 & 2 \\ 3 & 2 \end{array}] x + [\begin{array}{c} 1 \\ - 1 \end{array}]$

Step 1

Reorder factors in $X = [\begin{array}{c} 1 & 2 \\ 3 & 2 \end{array}] x + [\begin{array}{c} 1 \\ - 1 \end{array}]$ .

$X = x [\begin{array}{c} 1 & 2 \\ 3 & 2 \end{array}] + [\begin{array}{c} 1 \\ - 1 \end{array}]$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Multiply $x$ by each element of the matrix.

$X = [\begin{array}{c} x \cdot 1 & x \cdot 2 \\ x \cdot 3 & x \cdot 2 \end{array}] + [\begin{array}{c} 1 \\ - 1 \end{array}]$

Step 2.2

Simplify each element in the matrix.

Tap for more steps...

Step 2.2.1

Multiply $x$ by $1$ .

$X = [\begin{array}{c} x & x \cdot 2 \\ x \cdot 3 & x \cdot 2 \end{array}] + [\begin{array}{c} 1 \\ - 1 \end{array}]$

Step 2.2.2

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

$X = [\begin{array}{c} x & 2 x \\ x \cdot 3 & x \cdot 2 \end{array}] + [\begin{array}{c} 1 \\ - 1 \end{array}]$

Step 2.2.3

Move $3$ to the left of $x$ .

$X = [\begin{array}{c} x & 2 x \\ 3 x & x \cdot 2 \end{array}] + [\begin{array}{c} 1 \\ - 1 \end{array}]$

Step 2.2.4

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

$X = [\begin{array}{c} x & 2 x \\ 3 x & 2 x \end{array}] + [\begin{array}{c} 1 \\ - 1 \end{array}]$

Step 3

Move all terms containing a variable to the left side.

Tap for more steps...

Step 3.1

Subtract $[\begin{array}{c} x & 2 x \\ 3 x & 2 x \end{array}]$ from both sides of the equation.

$X - [\begin{array}{c} x & 2 x \\ 3 x & 2 x \end{array}] = [\begin{array}{c} 1 \\ - 1 \end{array}]$