Question

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

Answer 1

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]

Answer 2

[-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]