SOLUTION: Solve matrix equation for x: 3x+A=B Help, don't understand how to do this one. Can anyone show me step by step how to do this?

Algebra ->  Matrices-and-determiminant -> SOLUTION: Solve matrix equation for x: 3x+A=B Help, don't understand how to do this one. Can anyone show me step by step how to do this?      Log On


   

Question 153909: Solve matrix equation for x: 3x+A=B
Help, don't understand how to do this one. Can anyone show me step by step how to do this?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
It's easier to show if you have some matrices but I'll make them up here for example.
Let
A=%28matrix%282%2C2%2C2%2C1%2C0%2C1%29%29
B=%28matrix%282%2C2%2C5%2C9%2C3%2C4%29%29
x=%28matrix%282%2C2%2Cx%5B1%5D%2Cx%5B2%5D%2Cx%5B3%5D%2Cx%5B4%5D%29%29
From that, then
3x=%28matrix%282%2C2%2C3x%5B1%5D%2C3x%5B2%5D%2C3x%5B3%5D%2C3x%5B4%5D%29%29

Solve each matrix element equation for x%5Bi%5D,
3x%5B1%5D%2B2=5
3x%5B1%5D=3
x%5B1%5D=1
.
.
.
3x%5B2%5D%2B1=9
3x%5B2%5D=8
x%5B2%5D=8%2F3
.
.
.
3x%5B3%5D=3
x%5B3%5D=1
.
.
.
3x%5B4%5D%2B1=4
3x%5B4%5D=3
x%5B4%5D=1
Plugging in all the values,
x=%28matrix%282%2C2%2C1%2C8%2F3%2C1%2C1%29%29