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# Common Core Standard HSN-VM.C.6 Questions

(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

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Which of the following operations would result in a 2-by-2 matrix, with only the first and third points as elements? Let this matrix be called B.
1. $B = [[1,0,1,0,0],[1,0,1,0,0]] A$
2. $B = A [[1,1],[0,0],[1,1],[0,0],[0,0]]$
3. $B = A [[1,0],[0,0],[0,1],[0,0],[0,0]]$
4. $B = [[1,0,0,0,0],[0,0,1,0,0]] A$

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Which of the following matrix equations correctly represents this system of equations?
$4x + 3y - z = 12, \ \ 3y+x+z= 10, \ \ 8x - z - 3y = 1$
1. $[[4,3,-1],[3,1,1],[8,-1,-3]] [[x],[y],[z]] = [[12],[10],[1]]$
2. $[[4,3,-1],[3,1,1],[8,-1,-3]] [[12],[10],[1]] = [[x],[y],[z]]$
3. $[[4,3,-1],[1,3,1],[8,-3,-1]] [[x],[y],[z]] = [[12],[10],[1]]$
4. $[[4,1,8],[3,3,-3],[-1,1,-1]] [[x],[y],[z]] = [[12],[10],[1]]$
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. $[[2,0,,8],[1,3,,6]]$
Which augmented matrix represents the system of equations $3y+8x=16$ and $2x-4y=7$?
1. $[[3,8,,16],[2,-4,,7]]$
2. $[[16,8,,3],[7,-4,,2]]$
3. $[[8,3,,16],[2,-4,,7]]$
4. $[[7,-4,,2],[16,8,,3]]$
Jack is keeping track of the scores for his favorite teams in a series of basketball games. He records the initials of the team and score for each game. Which matrix represents the data he collected?
Round 1
SC 67
RG 103
PD 89

Round 2
RG 109
SC 86
PD 111

Round 3
PD 42
SC 99
RG 121
1. $[[67,103,89],[109,86,111],[42,99,121]]$
2. $[[67,86,99],[103,109,121],[89,111,42]]$
3. $[[42,99,121],[111,86,109],[67,103,89]]$
4. $[[67,109,42],[103,86,99],[89,111,122]]$
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. $[[2,32,,5],[14,-3,,4]]$
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. $[[1,18,,-1],[1,2,,-4]]$