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# Matrices Questions - All Grades

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What is the rule for matrix multiplication?
1. The number of columns of the first matrix must equal the number of rows of the second matrix
2. The matrices must have the same dimensions.
3. The matrices must have the same number of rows, but not columns.
4. There is no rule. Matrix multiplication is always possible.
What is the rule for matrix addition and subtraction?
1. The number of columns of the first matrix must equal the number of rows of the second matrix
2. The matrices must have the same dimensions.
3. The matrices must have the same number of rows, but not columns.
4. There is no rule. Matrix addition and subtraction is always possible.
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 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. $[[2,0,8],[1,3,6]]$
Evaluate, if possible. $[[-5,7],[6,8]] - [[4,0,-2],[9,0,1]]$
1. $[[-9,7],[-3,8]]$
2. $[[13,-7],[3,-8]]$
3. $[[-9,7,4],[-3,8,-13]]$
4. Impossible
Find the product, if possible. $[[2,0],[-3,5],[1,4]]*[[3],[-2]]$
1. $[[6,-19,-5]]$
2. $[[6],[-19],[-5]]$
3. $[[5,-5],[0,3]]$
4. Impossible
Perform the indicated operations. If the matrix does not exist, write impossible.

$[[8,3],[-1,-1]]-[[0,-7],[6,2]]$
1. $[[-8,-10],[-7,-3]]$
2. $[[-3,10],[-7,8]]$
3. $"Impossible"$
4. $[[8,10],[-7,-3]]$
Find the inverse of the matrix, if it exists.

$[[-4,-2],[7,8]]$
1. $"Does Not Exist"$
2. $[[4/9,1/9],[-7/18,-2/9]]$
3. $[[2/9,1/9],[-7/18,-4/19]]$
4. $[[-4/9,-1/9],[7/18,2/9]]$
The matrix $[[1,2,3],[4,5,6],[7,8,9]]$ multiplied by the vector $< 1,2,3 >$ equals:
1. $[[1,4,9],[4,10,18],[7,16,27]]$
2. $[ [14],[32],[50]]$
3. $[[12],[30],[54]]$
4. $[[1,2,3],[8,10,12],[21,24,27]]$
If the matrix $[[2,9,8],[0,3,4],[1,11,3]]$ is multiplied by the scalar $5$, what is the result?
1. $[[7,14,13],[5,8,9],[6,16,8]]$
2. $[[10,45,40],[0,15,20],[5,55,15]]$
3. $[[3,4,1],[11,3,2],[9,8,0]]$
4. $[[10,0,5],[45,15,55],[40,20,15]]$
Which matrix would transform the vector $< 4,2,7 >$ to the vector $<20,23,51 >$ ?
1. $[[0,3,2],[4,0,1],[3,2,5]]$
2. $[[3,2,5],[4,0,1],[0,3,2]]$
3. $[[0,4,3],[3,0,2],[2,1,5]]$
4. $[[5,1,2],[2,0,3],[3,4,0]]$
$[[5,2],[2,1]]-[[2,1],[4,-3]] =$
1. $[[3,1],[2,4]]$
2. $[[7,3],[6,-2]]$
3. $[[12,6],[2,1]]$
4. $[[3,1],[-2,4]]$
Evaluate the determinant using diagonals.

$[[-5,-6,7],[4,0,5],[-3,8,2]]$
1. $562$
2. $-80$
3. $26$
4. $-561$
$[[0,2],[5,1]]+[[4,2],[2,7]] =$
1. $[[4,4],[7,8]]$
2. $[[4,0],[3,6]]$
3. $[[2,9],[9,3]]$
4. $[[0,12],[45,9]]$