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# Common Core Standard HSA-REI.C.8 Questions

(+) Represent a system of linear equations as a single matrix equation in a vector variable.

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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. $[ [3,8,-23],[34,-2,53],[18,51,4] ]*[[x],[y],[z]]*[[14],[102],[16]]$
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. $[ [0,2,15],[2,-12,-3],[53,1,24] ]*[[x],[y],[z]]=[[11],[7],[32]]$
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. $[ [6,2,19],[1,-3,-12],[18,0,14] ]*[[x],[y],[z]]*[[26],[17],[18]]$
Which matrices below properly represent the system of equations?
$13x+5y+3z=28$, $4x-2z+3z=12$, $15x+52y+4y=13$
1. $[[13,5,3],[4,0,1],[15,56,0]]*[[x],[y],[z]]=[[28],[12],[13]]$
2. $[[3,1,0],[5,0,56],[13,4,15]]*[[x],[y],[z]]=[[28],[12],[13]]$
3. $[ [3,5,13],[1,,54],[,56,15] ]*[[z],[y],[x]]=[[13],[12],[28]]$
4. $[ [13,5,3],[4,0,1],[15,56,0] ]*[[x],[y],[z]]*[[13],[12],[28]]$
$9x+12y+34z=23$, $z+2x+8-2y=9$, $5x+14z+3y=15$
1. $[ [9,2,5],[12,-2,14],[34,1,3] ]*[[x],[y],[z]]=[[23],[1],[15]]$
2. $[ [9,2,5],[12,-2,14],[34,1,3] ]*[[x],[y],[z]]=[[23],[9],[15]]$
3. $[ [9,12,34],[2,-2,1],[5,3,14] ]*[[x],[y],[z]]=[[23],[1],[15]]$
4. $[ [9,12,34],[2,-2,1],[5,14,3] ]*[[x],[y],[z]]=[[23],[9],[15]]$