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# Using Matrices for Systems of Linear Equations (Grades 11-12)

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## Using Matrices for Systems of Linear Equations

1.
Which matrices below properly represent the system of equations?
$3x+8y-23z=14$, $34x-2y+53z=102$, $18x+51y+4z=16$
1. $[[3,34,18],[8,-2,51],[-23,53,4]]*[[x],[y],[z]]=[[14],[102],[16]]$
2. $[[3,8,-23],[34,-2,53],[18,51,4]]*[[x],[y],[z]]=[[14],[102],[16]]$
3. $[ [3,34,18],[8,-2,51],[-23,53,4] ]*[[z],[y],[x]]=[[16],[102],[14]]$
4. $[ [3,8,-23],[34,-2,53],[18,51,4] ]*[[x],[y],[z]]*[[14],[102],[16]]$
2.
Which matrices below properly represent the system of equations?
$19z+2y+34z-8=32$, $z+2x+4-12y=7$, $15x+24z-3y=11$
1. $[ [0,2,32],[2,-12,7],[15,-3,24] ]*[[x],[y],[z]]=[[32],[7],[11]]$
2. $[ [0,2,53],[2,-12,1],[15,-3,24] ]*[[x],[y],[z]]=[[40],[3],[11]]$
3. $[ [0,2,53],[2,-12,1],[15,-3,24] ]*[[z],[y],[x]]=[[40],[3],[11]]$
4. $[ [0,2,15],[2,-12,-3],[53,1,24] ]*[[x],[y],[z]]=[[11],[7],[32]]$
3.
Which matrices below properly represent the system of equations?
$19z+2y+6x=26$, $x-12z-3y=17$, $5x+14z+13x-5=13$
1. $[ [6,1,18],[2,-3,0],[19,-12,14] ]*[[x],[y],[z]]=[[18],[17],[26]]$
2. $[ [6,1,18],[2,-3,0],[19,-12,14] ]*[[x],[y],[z]]=[[26],[17],[18]]$
3. $[ [6,1,18],[2,-3,0],[19,-12,14] ]*[[z],[y],[x]]=[[26],[17],[13]]$
4. $[ [6,2,19],[1,-3,-12],[18,0,14] ]*[[x],[y],[z]]*[[26],[17],[18]]$
4.
Find the solution of the following matrix equation $[[1,5],[1,6]][[x],[y]]=[[-4],[-5]]$.
1. $(1,-1)$
2. $(1,1)$
3. $(0,1)$
4. $(-1,-1)$
5.
Solve. $[[5,4],[-2,-3]] [[x],[y]] = [[6],[-1]]$

6.
Which augmented matrix represents the system of equations $2x+5y=32$ and $4x-3y=14$?
1. $[[-2,-5,, -32],[-4,3,, -14]]$
2. $[[2,5,,32],[4,-3,,14]]$
3. $[[32,5,,2],[4,-3,,14]]$
4. $[[2,32,,5],[14,-3,,4]]$
7.
Which augmented matrix represents the system of equations $y-x=18$ and $x-4=2y$?
1. $[[1,-2,,4],[-1,1,,18]]$
2. $[[1,-1,,18],[1,2,,-4]]$
3. $[[18,-1,,1],[2,-4,,1]]$
4. $[[1,18,,-1],[1,2,,-4]]$
8.
Which augmented matrix represents the system of equations $2x=8$ and $6=3y+x$?
1. $[[2,8,,0],[6,3,,1]]$
2. $[[8,2,,0],[6,3,,1]]$
3. $[[0,2,,8],[6,3,,1]]$
4. $[[2,0,,8],[1,3,,6]]$
9.
Find the row-reduced echelon form of the following augmented matrix to find the solution to the corresponding system of equations.
$[[2,1,,13],[1,-5,,-10]]$
1. $(10,3)$
2. $(13,-33)$
3. $(5,3)$
4. No solution
10.
Use Gaussian Elimination to find the Row-Reduced Echelon form of the following matrix, thus solving the corresponding system of equations.
$[[3,-2,,-20],[-5,1,,17]]$

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