Matrix equations not requiring inverses. [-5,31,32,30]=[3,-5,0,-2] 4x

[-5, - 31, 32, 30] = [3, - 5, 0, - 2] + 4x

4x = [-5 - 3, - 31 + 5, 32, 30 + 2] = [-8, - 26, 32, 32]

x = [-8/4, - 26/4, 32/4, 32/4]

x = [-2, - 13/2, 8, 8]

Below is the solution:

Get rid of right hand side row vector so take it to other sides then signs of all its terms will invert.

[-5,31,32,30]=[3,-5,0,-2]+4X

[-5,31,32,30] - [3,-5,0,-2] = 4X

Subtract respective terms of second row matric from first one. i. e.

[-5 - (3), 31 - (-5), 32 - (0), 30 - (-2) ] = 4X

since multiplication of two negative signs result in positive sign so;

[-5-3, 31+5,32-0,30+2] = 4X

[-8, 36,32,32] = 4X

4 is just a scalar number so we can divide both sides with 4 to get rid of 4 from right hand side.

therefore;

[-8/4, 36/4,32/4,32/4] = 4X/4

[-2,9,8,8]=X

Result is:

X=[-2,9,8,8]