Linear Algebra Examples

$3 a + 5 b + 2 d = 0$ , $4 a + 7 b + 5 d = 0$ , $a + b - 4 d = 0$ , $2 a + 9 b + 6 d = 0$

Step 1

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

$[\begin{array}{c} 3 & 5 & 2 \\ 4 & 7 & 5 \\ 1 & 1 & - 4 \\ 2 & 9 & 6 \end{array}] \cdot [\begin{array}{c} a \\ b \\ d \end{array}] = [\begin{array}{c} 0 \\ 0 \\ 0 \\ 0 \end{array}]$

Step 2

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

Step 3

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

Step 4

Simplify the left and right side.

$[\begin{array}{c} a \\ b \\ d \end{array}] =$

Step 5

Find the solution.

$a =$

$b =$

$d =$