[MOVED] solving system of linear equations

[thelazyman]

I am needing some help solving a matrix equation. I got up to this:

4m -5p = 1
-18m +n +24p =2
-3m +4p = 3

I do not know how they got:

m = 19
n = -16
p = 15

Please someone help.

Thanks

 

[stapel]

Since we do not have the original exercise, nor your work, we cannot judge where you might have made an error, nor if "they" were correct. Sorry.

Eliz.

 

[galactus]

There are many approaches, but I will just demonstrate one substitution method.

\(\displaystyle \L\\\begin{array}4m-5p=1\\-18m+n+24p=2\\-3m+4p=3\end{array}\)

Solve the 3rd equation for p and sub into the first:

\(\displaystyle \L\\-3m+4p=3\)

\(\displaystyle \L\\\frac{3+3m}{4}=p\)


\(\displaystyle \L\\4m-5(\frac{3+3m}{4})=1\)

\(\displaystyle \L\\4m-\frac{15}{4}-\frac{15}{4}m=1\)

\(\displaystyle \L\\\frac{1}{4}m-\frac{15}{4}=1\)

\(\displaystyle \L\\m=19\)

Now that you have m, you can easily use it in the first or third equation to find p, and so forth.