Question

99.2x+4y+0.3z=35.6
100x+71.8y+2.1z=50.4
100x+100y+98.4z+6.8q=71.3
x+y+z+q=1

find x,y,z and q!

Answer 1

This is the type of problem than when solved with normal algebra, takes multiple pages of work to finish. Of course, it can also be done with matrices. This is a particularly nasty problem, with four variables and decimals, so I won't even try the algebraic method. We will use matrices, with some help from a graphing calculator.

We will use two matrices, [A] and [B]. [A] will be a 4x4 matrix made of the coefficients from the four equations, like this:

99.2 4 0.3 0
100 71.8 2.1 0
100 100 98.4 6.8
1 1 1 1

[B] Will be a 4x1 matrix made up of the numbers to the right of each equals sign, like so:

35.6
50.4
71.3
1

After these are plugged into your graphing calculator, we can do a bit of math with them. The formula we will use is
\[[A]^{-1}*[B]\]
This returns this 4x1 matrix:

0.350
0.211
0.134
0.306

These are the four coordinates you end up with, x, y, z, and q, in that order. We can also express the answer as this ordered pair: (0.350, 0.211, 0.134, 0.306).

I hope this helps!

Answer 2

Thank you :)