Linear Algebra Examples

$- 2 x + 2 y + 3 z = 1$ , $x - y = 3$ , $y + 4 z = - 2$

Step 1

Find the $A X = B$ from the system of equations.

Step 2

The matrix must be a square matrix to find the inverse.

Inverse matrix cannot be found

Step 3

Left multiply both sides of the matrix equation by the inverse matrix.

Step 4

Any matrix multiplied by its inverse is equal to $1$ all the time. $A \cdot A^{- 1} = 1$ .

$[\begin{array}{c} x \\ y \\ z \end{array}] = I n v e r s e$ matrix cannot be $f o u n d \cdot [\begin{array}{c} 1 \\ 3 \\ - 2 \end{array}]$

Step 5

Simplify the right side of the equation.

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Multiply $I n v e r s e (m a t r i x) (c a n \cdot n o t) (b e) (f o u n d)$ by each element of the matrix.

Simplify each element in the matrix.

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Rearrange $I n v e r s e (m a t r i x) (c a n \cdot n o t) (b e) (f o u n d) \cdot 1$ .

Rearrange $I n v e r s e (m a t r i x) (c a n \cdot n o t) (b e) (f o u n d) \cdot 3$ .

Rearrange $I n v e r s e (m a t r i x) (c a n \cdot n o t) (b e) (f o u n d) \cdot - 2$ .

$[\begin{array}{c} I n^{4} v e^{3} r^{2} s m a^{2} t^{2} i x c o^{2} b f u d \\ 3 I n^{4} v e^{3} r^{2} s m a^{2} t^{2} i x c o^{2} b f u d \\ - 2 I n^{4} v e^{3} r^{2} s m a^{2} t^{2} i x c o^{2} b f u d \end{array}]$

Step 6

Simplify the left and right side.

$[\begin{array}{c} x \\ y \\ z \end{array}] = [\begin{array}{c} I n^{4} v e^{3} r^{2} s m a^{2} t^{2} i x c o^{2} b f u d \\ 3 I n^{4} v e^{3} r^{2} s m a^{2} t^{2} i x c o^{2} b f u d \\ - 2 I n^{4} v e^{3} r^{2} s m a^{2} t^{2} i x c o^{2} b f u d \end{array}]$

Step 7

Find the solution.

$x = I n^{4} v e^{3} r^{2} s m a^{2} t^{2} i x c o^{2} b f u d$

$y = 3 I n^{4} v e^{3} r^{2} s m a^{2} t^{2} i x c o^{2} b f u d$

$z = - 2 I n^{4} v e^{3} r^{2} s m a^{2} t^{2} i x c o^{2} b f u d$