SOLUTION: I am not understanding how to Solve the system of linear equation using matrices x+y+z=3 2x -z=7 5y+z=4 Can you guide me step by step in solving it?

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: I am not understanding how to Solve the system of linear equation using matrices x+y+z=3 2x -z=7 5y+z=4 Can you guide me step by step in solving it?      Log On


   

Question 412052: I am not understanding how to Solve the system of linear equation using matrices
x+y+z=3
2x -z=7
5y+z=4
Can you guide me step by step in solving it?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Note:  finding the value of a 3x3 matrix is done as follows:

%28matrix%283%2C3%2Ca1%2Cb1%2Cc1%2Ca2%2Cb2%2Cc2%2Ca3%2Cb3%2Cc3%29%29 = a1(b2c3-c2b3) - b1(a2c3-c2a3) + c1(a2b3-b2a3) 

x+y+z=3

2x -z=7

5y+z=4 



D = matrix%283%2C3%2C1%2C1%2C1%2C2%2C0%2C-1%2C0%2C5%2C1%29 = 13

    1*5 -1*2 +1*10 = 13

D%5Bx%5D+=+matrix%283%2C3%2C3%2C1%2C1%2C7%2C0%2C-1%2C4%2C5%2C1%29 = 39



D%5By%5D+=+matrix%283%2C3%2C1%2C3%2C1%2C2%2C7%2C-1%2C0%2C4%2C1%29 = 13



D%5Bz%5D+=+matrix%283%2C3%2C1%2C1%2C3%2C2%2C0%2C7%2C0%2C5%2C4%29 = -13



   x= 39/13 = 3  y = 13/13 = 1   z =-13/13 = -1