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# Matrices Questions - All Grades

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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. $[[2,0,,8],[1,3,,6]]$
Evaluate. $[(2, -3) , (-4, 2)]$ + $[ (-1, -5), ( 3, -2) ]$
1. $[(-1, -8), (-1, 0)]$
2. $[(1, -8), (-1,0)]$
3. $[(1, -8), (-7, 0)]$
4. None of the above
Evaluate. $[(2,-3), (-4,2)] - [(-1,-5), (-3,2)]$
1. $[(3,2),(-7,4)]$
2. $[(-3,2),(-7,4)]$
3. $[(3,2),(-1,0)]$
4. None of the above
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. $[[10,0,5],[45,15,55],[40,20,15]]$
Evaluate. $[[1,2],[3,4]]+[[1,2],[3,4]]$
1. $[[2,4],[6,8]]$
2. $[[2,8],[6,4]]$
3. $[[8,2],[6,4]]$
A square matrix A is NOT invertible (does not have an inverse) if which of the following is true?
1. Matrix A is the identity matrix
2. $A_{1,1} < 0$
3. Matrix A has any elements equal to zero
4. $det(A) = 0$
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.
Find the inverse of the matrix $[[1,2],[3,4]]$.
1. $[[-2,1],[3/2,-1/2]]$
2. $[[4,-2],[-3,1]]$
3. $[[4,2],[3,1]]$
4. $[[1,-2],[-3,4]]$
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.
Find the inverse of the matrix $[[2,5],[1,6]]$.
1. $[[42,-35],[-7,14]]$
2. $[[6/17,-5/17],[-1/17,2/17]]$
3. $[[2/7,5/7],[1/7,6/7]]$
4. $[[6/7,-5/7],[-1/7,2/7]]$
Find the inverse of the matrix $[[0,6],[2,8]]$.
1. $[[4/6,2/4],[2/12,6/0]]$
2. $[[-2/3,1/2],[1/6,0]]$
3. $[[0,1/2],[1/6,2/3]]$
4. $[[96,-72],[-24,0]]$
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. $[ [3,8,-23],[34,-2,53],[18,51,4] ]*[[x],[y],[z]]*[[14],[102],[16]]$
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. $[[67,109,42],[103,86,99],[89,111,122]]$
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