SOLUTION: A=[1 -1 0] [1 0 -1] [6 -2 -3] B=[-2 -3 1] [-3 -3 1] [-2 -4 1] Solve for x: 3X+4B=A If I could get some quick help it would be greatly appreciated. :)

Algebra ->  Trigonometry-basics -> SOLUTION: A=[1 -1 0] [1 0 -1] [6 -2 -3] B=[-2 -3 1] [-3 -3 1] [-2 -4 1] Solve for x: 3X+4B=A If I could get some quick help it would be greatly appreciated. :)      Log On


   



Question 751018: A=[1 -1 0]
[1 0 -1]
[6 -2 -3]
B=[-2 -3 1]
[-3 -3 1]
[-2 -4 1]
Solve for x: 3X+4B=A
If I could get some quick help it would be greatly appreciated. :)

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
A=[1 -1  0] 
  [1  0 -1]  
  [6 -2 -3] 

B=[-2 -3 1]
  [-3 -3 1]
  [-2 -4 1]

Solve for X: 3X+4B=A
3%22%22%2A%22%22X%22%22%2B%22%224%22%22%2A%22%22B%22%22=%22%22A

     3%22%22%2A%22%22X%22%22=%22%22A%22%22-%22%224%22%22%2A%22%22B

Consider the minus sign before the 4 as a plus sign times (-4).
That's because we'd rather add matrices than subtract them:

     3%22%22%2A%22%22X%22%22=%22%22A%22%22%2B%22%22%28-4%29%22%22%2A%22%22B

Substitute the matrices in the equation for the letters:

3%22%22%2A%22%22 X%22%22=%22%22%22%22%2B%22%22%28-4%29%22%22%2A%22%22

Distribute the (-4) by multiplying it by all 9 elements of the 
matrix on the far right:

3%22%22%2A%22%22 X%22%22=%22%22%22%22%2B%22%22

We add the corresponding elements of the matrices on the right:

3%22%22%2A%22%22 X%22%22=%22%22

Finally we multiply both sides by 1%2F3

%281%2F3%29%22%22%2A%22%223%22%22%2A%22%22X%22%22=%22%22%281%2F3%29%22%22%2A%22%22


Distribute the 1%2F3 by multiplying it by all 9 elements of the 
matrix on the right:

X%22%22=%22%22   

Edwin