Expert: Richard J. Raridon - 11/11/2005

Question
Dear Mr. Raridon,
   
   Good evening.  I am contacting you to ask if you can help me with some difficulty that I am having in College Algebra. I am also an AllExperts.com volunteer in the area of domestic violence, but today I have been so frustrated about this current chapter that we are in. I will list the specific problem(s) that I am having, but I also wanted to ask if you could just summarize and illustrate the proper ways to solve these matrices.

    Our instructor will not let us use a calculator, we have to use his software on our laptops called MathCAD, so on the test no calculators are allowed.
Here are a few problems that I need help in solving:

1.) {3x - 2y + 5z = 15}
    x - 2y - 2z = -1
    2x - 2y = 0

2.) {2x + 3y + 4z = 5}
    6x + 7y + 8z = 9
    2x + y + z = 1

3.) {x - y + z - w = -2}
    2x +   4z + w = 5
    2x - 3y + z  = -5
         y + 2z + 20w = 4

** I really pray that you can help me, thankyou.

My Regards,

Chardonnay Nicole Thomas
AllExperts.com

Answer
Well, I don't know what MathCAD does but you can solve these equations using determinants or the old fashioned way.  Doing it the old fashioned way with the first set, eliminate z by combining the first two equations to get 11x-14y = 25.
Combine that with the third equation to get x=y = -25/3 and z = 14/3.  You don't need a calculator for that.  If you want to use determinants, then evaluate the denominator determinant which is
3 -2 5
1 -2 -2
2 -2 0
and call that value D
then x = the value of the determinant
15 -2 5
-1 -2 -2
0 -2 0
divided by D.  
for y, replace the middle column and for z, replace the last column.