Matrices in Math

<p>Well I remember there was a matrix question the last time I took the ACT and I think I missed that one. According to Sparknotes, you only have to know how to add or subtract matrices. But on the test, I think it asked about setting up matrices to solve a problem. Can anyone teach me how to do that? Can you give me an example problem?</p>

<p>If you’re talking about a problem with three unknowns, it would go something like this:</p>

<p>Problem: Set up a matrix to solve for x, y, and z.</p>

<p>2x+3y+4z=10
5x-2y+3z=30
7x+2y-z=15</p>

<p>Your answer would be:</p>

<p>[2 3 4] [10]<br>
[5 -2 3] [y] = [30]
[7 2 -1] [z] [15]</p>

<p>(the formatting is weird, but basically the 3x3 matrix of the x,y,z coefficients multiplied by a 3x1 matrix of x,y,z equals the 3x1 matrix of the three answers.)</p>

<p>there’s matrices on the ACT?</p>

<p>^ Yeah. I encountered one and totally forgot what to do (I took the ACT in June of my junior year after taking calculus… I was so mad at myself because of it.)</p>

<p>Example:</p>

<p>5x +3y - 6z = 1
10x - 6y + 3z = -1
-5x - 9y + 6z = -5</p>

<p>type into a graphing calculator for matrix a like so
[5 3 -6 1]
[10 -6 3 -1]
[-5 -9 6 -5]</p>

<p>First column is x’s, second is y’s, third is z’s, forth is answers</p>

<p>the look for rref (reduced row echelon form) in your matrix math functions</p>

<p>type in: rref[a]</p>

<p>answer is
[1 0 0 1/5]
[0 1 0 2/3]
[0 0 1 1/3]</p>

<p>the last column is answers</p>

<p>(1/5, 2/3, 1/3)
rref is basically a shortcut that assures the right answer</p>

<p>^^do they ask those types of questions, or like adding and subtracting matrices?</p>