Twelfth Grade (Grade 12) Matrices Questions for Tests and Worksheets

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Grade 12 Matrices CCSS: HSN-VM.C.11

What does the matrix

$[[2,6,1],[4,1,8]]$ multiplied by the vector

$<< 4,10,-5 >>$ equal?

$[[8,60,-5],[16,10,-40],[0,0,0]]$
$[ [16,10,-40],[8,60,-5]]$
$[[24],[70],[-45]]$
$[[63],[-14]]$

Grade 12 Matrices CCSS: HSN-VM.C.12

For the vertex matrix

$V = [[1,1,3,3],[-1,2,2,-1]]$ and transformation matrix

$M = [[1,2],[0,1]]$ , what is the resulting shape if M is applied to V? Choose the most specific classification possible.

Square
Parallelogram
Rectangle
Quadrilateral

Grade 12 Matrices CCSS: HSN-VM.C.12

Which of the following equations correctly state that, for a figure in the cartesian plane, a reflection over the x-axis, followed by a reflection over the y-axis, is identical to a 180° rotation (either clockwise or counterclockwise)?

$[[1,0],[0,1]] [[-1,0],[0,-1]] = [[-1,0],[0,-1]]$
$[[1,0],[0,-1]] [[-1,0],[0,1]] = [[0,1],[1,0]]$
$[[-1,0],[0,1]] [[1,0],[0,-1]] = [[-1,0],[0,-1]]$
$[[1,0],[0,-1]] [[-1,0],[0,1]] = [[-1,0],[0,-1]]$

Grade 12 Matrices CCSS: HSN-VM.C.10

Sarah has been given the following matrix equation to solve,

$A x = b$ , where A is a 3-by-3 matrix, b is a 3-by-1 matrix, and x is a 3-by-1 matrix. If she knows the equation can be solved by multiplying the inverse of A on both sides of the equation, which of the following must be true?

A must be a diagonal matrix (its off-diagonal entries must be zero).
The matrix b must also have an inverse.
The determinant of A is not equal to zero.
More than half of the elements in the matrix A are non-zero.

Grade 12 Matrices CCSS: HSN-VM.C.10

Given a matrix A, is there always another matrix, B, such that their sum is the zero matrix? What are the elements of the matrix B?

No, there isn't always such a matrix B. If there is, its elements are the negative of the corresponding elements in matrix A.
No, there isn't always such a matrix B. If there is, its elements are determined on a case-by-case basis, with no general rule.
Yes, there is always such a matrix. The elements of B are found on a case-by-case basis, with no general rule.
Yes, there is always such a matrix. The elements of B are the negative of the corresponding elements in A.

Grade 12 Matrices CCSS: HSN-VM.C.9

Which of the following are always true for matrices

$A, B,$ and

$C ?$ Choose all that apply.

$(AB)C = A(BC)$
$A(B+C) = AB + AC$
$AB + C = C + BA$
$A(B + C) = (B + C)A$

Grade 12 Matrices CCSS: HSN-VM.C.8

Multiply, if possible.

$[[4,0],[-3,6]] * [[3,-4],[5,1]]$

$[[12,0],[-15,6]]$
$[[12,20],[-33,-9]]$
$[[12,-16],[21,18]]$
Not possible.

Grade 12 Matrices CCSS: HSN-VM.C.7

For

$M = [[3,9],[5,1]]$ , what is the result of multiplying

$M$ by 3?

$[[9,9],[5,1]]$
$[[9,27],[15,3]]$
$[[9,27],[5,1]]$
$[[9,9],[15,1]]$

Grade 12 Matrices CCSS: HSN-VM.C.8

Evaluate.

$[[5,0,-3,-2,1]] + [[-2,0,-5,7,1]]$

$[[5,-2,-5,7,1]]$
$[[7,0,8,9,2]]$
$[[6,7,-8,-2,1]]$
$[[3,0,-8,5,2]]$

Grade 12 Matrices CCSS: HSN-VM.C.6

Clayton is recording information for a science experiment. He has three separate plants in different areas, and is recording their height each week. So far he has recorded data for four weeks, and each plant always increased in height. The heights of the first plant are 3 cm, 6 cm, 8 cm, 12 cm. The heights of the second plant are 2 cm, 4 cm, 5 cm, 7 cm. The heights of the third plant are 2 cm, 5 cm, 8 cm, 10 cm. Which of the following matrices correctly represent this data? Choose all that apply.

$[[3,6,8,12],[2,4,5,7],[2,5,8,10]]$
$[[3,2,2],[6,4,5],[8,5,8],[12,7,10]]$
$[[2,2,3],[4,5,5],[6,7,8],[8,10,12]]$
$[[12,8,6,3],[7,5,4,2],[2,5,8,10]]$

Grade 12 Matrices CCSS: HSN-VM.C.10

$I$ is the identity matrix, and

$A$ has the same dimensions as

$I$ , then

$AI = IA$ .

True
False

Grade 12 Matrices CCSS: HSN-VM.C.9

For the matrix expression

$A (B + C)$ , the following is given:

$AB = [[7,24],[63,54]], \ \ AC = [[20,-2],[72,18]]$ . What is

$A (B + C)$ equal to?

Not enough information to determine this.
$[[27,22],[135,72]]$
$[[1868,418],[5148,846]]$
$[[13.5, 11],[67.5, 36]]$

Grade 12 Matrices CCSS: HSN-VM.C.8

Kathi recently did a survey, asking which grocery store people shopped at most frequently. There were 5 possible grocery stores to choose from. She asked 3 different groups of people and then put this data in a matrix, each row representing a different group of people, each column representing a different grocery store. Let this be matrix G. Kathi wants to find a matrix, A, such that

$G \ A = S$ , where the matrix S will be the sum of each row (or the total number of people in each group). Which of the following would correctly accomplish this?

$A = [[1,1,1,1,1]]$
$A = [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]$
$A = [[1],[1],[1],[1],[1]]$
Without knowing the entries of matrix G, this cannot be determined.

Grade 12 Matrices CCSS: HSN-VM.C.9

For the matrices

$A = [[3,4,-1],[0,1,0],[-3,-4,9]], B = [[1,1,1],[1,1,1],[1,1,1]]$ ,

$AB = BA .$

True
False

Grade 12 Matrices CCSS: HSN-VM.C.8

Subtract.

$[[4,8],[7,2]] - [[3,9],[3,6]]$

$[[1,-1],[4,-4]]$
$[[-5,5],[1,-1]]$
$[[7,17],[10,8]]$
$[[1,8],[4,3]]$

Grade 12 Matrices CCSS: HSN-VM.C.7

For

$A = [[1,7],[0,3]]$ , which of the following is equal to

$4A ?$

$[[4,28],[4,12]]$
$[[4,7],[0,3]]$
$[[4,28],[0,12]]$
$[[4,7],[4,3]]$

Grade 12 Matrices CCSS: HSN-VM.C.7

For

$D = [[3, -4, 0],[2,1/2,-5]]$ , find

$-6D$ .

$[[18,-4,0],[-12,1/2,-5]]$
$[[18,-24,-6],[2,1/2,-5]]$
$[[-18,24,0],[-12,-3,30]]$
$[[18,-24,-6],[12,3,-30]]$

Grade 12 Matrices CCSS: HSN-VM.C.7

For

$M = [[3,0,-9],[6,-6,12],[1,15,-3]]$ find

$4/3 M$ .

$[[4,0,-12],[6,-6,12],[1,15,-3]]$
$[[4,0,-9],[8,-6,12],[4/3,15,-3]]$
$[[4,4/3,-12],[8,-8,16],[4/3,20,-4]]$
$[[4,0,-12],[8,-8,16],[4/3,20,-4]]$

Grade 12 Matrices CCSS: HSN-VM.C.8

Evaluate.

$[[1,0,0],[0,1,0],[0,0,1]] + [[1,0,-9],[-5,2,5],[7,-2,3]]$

$[[2,1,-8],[-4,3,6],[8,-1,4]]$
$[[2,0,9],[5,3,5],[7,2,3]]$
$[[2,0,-9],[-5,3,5],[7,-2,4]]$
$[[1,0,-9],[-5,2,5],[7,-2,3]]$

Grade 12 Matrices CCSS: HSN-VM.C.6

Kiera has a few apple trees, peach trees, and pear trees. She has kept track of the total volume of fruit, in bushels, each fruit tree has produced for the years 2016, 2017, and 2018. She has put this in a matrix, where each type of fruit tree is in a different column (apples, peaches, and pears, respectively), and each row is a certain year, starting with 2016 as the first row. Let this be matrix F.

$F =[[45, 6, 12],[40, 3, 10],[50, 5, 15]]$

Which operation would give the total volume of fruit produced, in bushels, for each year?

$[[1,1,1]] F$
$[[1],[1],[1]] F$
$F [[1,1,1]]$
$F [[1],[1],[1]]$

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Twelfth Grade (Grade 12) Matrices Questions