How do I solve matrices? simple and complex?

Question

help!!!! · Answer

any examples?

agreene · Answer

this might be helpful: http://www.mathsisfun.com/algebra/systems-linear-equations-matrices.html

anonymous · Answer

Hi, 

If you have a graphing calculator, make a 4 x 5 matrix and enter these numbers with 0 for anything missing: 

[1 . 1 . 1 . 1 . 0] 
[8 .-1 . 8 .-1 . 0] 
[3 . 3 .-1 . 3 .-4] = [A] 
[1 .-2 . 3 .-1 . 0] 

Use the matrix command under math 

rref([A]) 

This will solve the system for you. 

[1 . 0 . 0 . 0 . -1] 
[0 . 1 . 0 . 0 . .2] 
[0 . 0 . 1 . 0 . .1] 
[0 . 0 . 0 . 1 . -2] 

The answer is x = -1, y = 2, z = 1, and w = -2. 

Without a calculator, it is a much longer process. 

[1 . 1 . 1 . 1 . 0] <=Multiply by -8 and add this to row 2. 
[8 .-1 . 8 .-1 . 0] 
[3 . 3 .-1 . 3 .-4] 
[1 .-2 . 3 .-1 . 0] 

[1 . 1 . 1 . 1 . 0] <=Multiply by -3 and add this to row 3. 
[0 .-9 . 0 .-9 . 0] 
[3 . 3 .-1 . 3 .-4] 
[1 .-2 . 3 .-1 . 0] 

[1 . 1 . 1 . 1 . 0] <=Multiply by -1 and add this to row 4. 
[0 .-9 . 0 .-9 . 0] 
[0 . 0 .-4 . 0 .-4] 
[1 .-2 . 3 .-1 . 0] 

[1 . 1 . 1 . 1 . 0] 
[0 .-9 . 0 .-9 . 0] 
[0 . 0 .-4 . 0 .-4] 
[0 .-3 . 2 .-2 . 0] 

Multiply row 2 by -1/9 to get a 1 in the 2nd row, 2nd column. 

[1 . 1 . 1 . 1 . 0] 
[0 . 1 . 0 . 1 . 0] <=Multiply by -1 and add this to row 1. 
[0 . 0 .-4 . 0 .-4] 
[0 .-3 . 2 .-2 . 0] 


[1 . 0 . 1 . 0 . 0] 
[0 . 1 . 0 . 1 . 0] <=Multiply by 3 and add this to row 4. 
[0 . 0 .-4 . 0 .-4] 
[0 .-3 . 2 .-2 . 0] 

[1 . 0 . 1 . 0 . 0] 
[0 . 1 . 0 . 1 . 0] 
[0 . 0 .-4 . 0 .-4] 
[0 . 0 . 2 . 1 . 0] 

Divide row 3 by -4 to get a 1 in the 3rd row, 3rd column. 

[1 . 0 . 1 . 0 . 0] 
[0 . 1 . 0 . 1 . 0] 
[0 . 0 . 1 . 0 . 1] <=Multiply by -1 and add this to row 1. 
[0 . 0 . 2 . 1 . 0] 

[1 . 0 . 0 . 0 .-1] 
[0 . 1 . 0 . 1 . 0] 
[0 . 0 . 1 . 0 . 1] <=Multiply by -2 and add this to row 4. 
[0 . 0 . 2 . 1 . 0] 

[1 . 0 . 0 . 0 .-1] 
[0 . 1 . 0 . 1 . 0] 
[0 . 0 . 1 . 0 . 1]. 
[0 . 0 . 0 . 1 .-2] <=Multiply by -1 and add this to row 2. 

[1 . 0 . 0 . 0 .-1] 
[0 . 1 . 0 . 0 . 2] 
[0 . 0 . 1 . 0 . 1]. 
[0 . 0 . 0 . 1 . -2] 

The answer is x = -1, y = 2, z = 1, and w = -2 

I hope that helps!! :-)