# write without matrix[1  -2  0] [x1]     [ 3][-3  1 -1] [x2] = [-2][2    0 4] [x3]     [ 5]

sciencesolve | Certified Educator

Using the multiplication of matrices of different dimensions yields:

`x_1 - 2x_2 + 0x_3 = 3`

`-3x_1 + x_2 - x_3 = -2`

`2x_1 + 0x_2 + 4x_3 = 5`

Consider the first and the second equations and use elimination to remove `x_2` .

Multiply the second equation by the opposite of the coefficient of `x_2`  from the first equation.

`x_1 - 2x_2 = 3`

`` `-6x_1 + 2x_2 -2x_3 = -4`

`-5x_1 - 2x_3 = -1`

Consider the equation `-5x_1 - 2x_3 = -1`  and the third equation and use elimination procedure. Multiply the equation `-5x_1 - 2x_3 = -1`  by 2.

`-10x_1 - 4x_3 = -2`

Add this equation to the third original equation:

`-10x_1 - 4x_3 + 2x_1 + 4x_3 =-2 +5`

`` `-8x_1 = 3 =gt x_1 = -3/8`

`` `2*(-3/8) + 4x_3 = 5 =gt -3/4 + 4x_3 = 5`

Add 3/4 both sides: `4x_3 = 5 + 3/4 =gt 4x_3 = 23/4 =gt x_3 = 23/16`

`x_1 - 2x_2 = 3 =gt -2x_2 = 3/8 + 3 =gt -2x_2 = 27/8 =gt x_2 = -27/16`

The elements of the column matrix are`x_1 = -3/8; x_2 = -27/16 ; x_3 = 23/16.`