Matrices Questions for Tests and Worksheets

Select All Questions

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

In Leane's math homework, she has to multiply three matrices together by hand, as follows:

$[[8,2,0],[-4,7,-3]] * [[4,7,-4,-2],[1,3,8,7],[-5,-3,6,6]] * [[-6],[5],[-4],[1]]$ . She decides that if she multiplies the last two matrices together first, it will make the computation easier. Is she correct? Why or why not.

No, she cannot do this. She has to multiply the first two matrices together first, and then the third, according to normal evaluating rules.
Although she is allowed to do this, it will not make the computation easier. Regardless of how she multiplies these matrices, the answer will be a 2-by-1 matrix, and the same work will be involved either way.
Yes, she can do this, and it will make the computation easier. Multiplying the second and third matrices together first, and then the first by the product just found, will reduce the total number of arithmetic computations (multiplication and addition) to be performed.
These matrices are not able to be multiplied together, as they have incompatible dimensions.

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

Adrian was learning about the identity matrix and multiplicative inverses in math class, and is now working on his homework. He knows that, for a square matrix

$A$ , he can usually find another matrix

$B$ such that

$AB = I$ , where

$I$ is the identity matrix of the same size as

$A$ and

$B$ . Adrian is now considering the matrix

$A = [[3,2],[6,4]]$ . The way he has been finding the multiplicative inverse matrix is to create another matrix

$B = [[a,b],[c,d]]$ . He performs this multiplication, and it yields two systems of equations, as follows.

${{:(3a + 2c , = 1),(6a + 4c, = 0):}$

${{:(3b + 2d , = 0),(6b + 4d, = 1):}$

Adrian realizes that both these systems are inconsistent. Is Adrian's work correct? And if so, what does this imply?

No, Adrian's work is not correct. His entire method for finding multiplicative inverses is wrong.
No, Adrian's work is not correct. Although his general method is OK, he has made a mistake when multiplying the matrices.
Yes, Adrian's work is correct. This means that, in this case, no such B matrix exists, and therefore not all square matrices have a multiplicative inverse.
Yes, Adrian's work is correct. This implies that, in this case, the B matrix must be the zero matrix.

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

Multiply, if possible.

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

$[[3,0,-1],[0,-27,2],[15,12,5]]$
$[[2,-14,28],[1,-25,53],[-2,-22,32]]$
$[[-5,-12,9],[-23,-22,18],[-25,-37,16]]$
$[[-6,-12,8],[-13,-21,17],[-26,-36,12]]$

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

Shane has a matrix of three ordered pairs,

$P = [[3,2],[8,-1],[5,0]]$ , where the x-coordinates are in the first column and the y-coordinates are in the second column. He wants to find a matrix A, such that the product

$A \ P$ gives a matrix that will only have the first and third ordered pairs. Which of the following matrices will give this result?

$A = [[1,1],[0,0],[1,1]]$
$A = [[1,0,0],[0,0,1]]$
$A = [[1,0,1]]$
$A = [[1,0,1],[1,0,1]]$

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

Can the following matrix expression be evaluated? Why or why not?

$[[3,-4],[0,-1],[9,1]] \ * ( [[0,1],[1,0]] + [[-5,-9],[-1,4]] )$

Yes, but only as is (one cannot distribute the 3-by-2 matrix).
Yes, either as is, or if the distributive property is applied.
No, after performing the addition of the two smaller matrices, the new dimensions will not allow for multiplication with the left-most matrix.
No, all matrices must be have the same dimensions.

Grade 11 Matrices CCSS: HSN-VM.C.8

Evaluate.

$[(2, -3) , (-4, 2)]$ +

$[ (-1, -5), ( 3, -2) ]$

$[(-1, -8), (-1, 0)]$
$[(1, -8), (-1,0)]$
$[(1, -8), (-7, 0)]$
None of the above

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

Multiply.

$[[2,-1],[0,7]] * [[-1,-4],[6,1]]$

$[[-8,-9],[42,7]]$
$[[-2,4],[0,7]]$
$[[1,-5],[6,8]]$
$[[-8,-27],[12,1]]$

Grade 12 Matrices CCSS: HSA-REI.C.9

Find the inverse of the matrix

$[[2,5],[1,6]]$ .

$[[42,-35],[-7,14]]$
$[[6/17,-5/17],[-1/17,2/17]]$
$[[2/7,5/7],[1/7,6/7]]$
$[[6/7,-5/7],[-1/7,2/7]]$

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

Multiply the following.

$[(0,2),(-2,-5)] * [(6,-6),(3,0)]$

Undefined
$[(0,6),(-27,12)]$
$[(6,0),(-27,12)]$
None of the above

Grade 11 Matrices CCSS: HSA-REI.C.9

Solve the matrix equation.

$[[3,4],[1,4/3]] [[x],[y]] = [[9],[4/3]]$

The inverse does not exist (the matrix is singular).
$(-640/27, 160/9)$
$(160/3,-40)$
$(416/3, 104)$

Grade 11 Matrices

Element

$"V"_{3,2}$ in Matrix V shown below is .

$V=[[12,7,21,31,11],[45,-2,14,27,19],[-3,15,36,71,26],[4,-13,55,34,15]]$

15
14
-2
36

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

Put the vertices of the shape in the graph below into a vertex matrix, and then apply the rotation matrix

$A = [[sqrt(2)/2, -sqrt(2)/2],[sqrt(2)/2, sqrt(2)/2]]$ . By what angle, measured in degrees, has the shape been rotated (given that the angle of rotation is counterclockwise)?

30°
45°
60°
105°

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

For the matrix

$A = [[1,0,0],[0,1,0],[0,0,0]]$ , what is the best description of how this transforms a vector with 3 components if they are multiplied together?

The vector stays the same.
The vector now only has 2 components.
The vector's third component is changed to zero.
At least one component of the vector is reduced to zero.

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

Given the triangle with vertices

$(1,1), (2,3),$ and

$(5,1)$ , which of the following matrix expressions would represent the reflection of this triangle over the y-axis?

$[[1,0],[0,-1]] \ [[1,1],[2,3],[5,1]]$
$[[-1,0],[0,1]] \ [[1,2,5],[1,3,1]]$
$[[-1,0],[0,1]] \ [[1,1],[2,3],[5,1]]$
$[[1,0],[0,-1]] \ [[1,2,5],[1,3,1]]$

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

This question is a part of a group with common instructions. View group »

What is the absolute value of the determinant of the transformation matrix,

$T ?$

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

Let

$vec{v}$ be a vector with 2 or more components and represented as a column matrix, and let

$A$ be a transformation matrix. When the transformation matrix is applied to

$vec{v}$ it results in a new vector,

$vec{w}$ . Which of the following correctly represents this?

$vec{w} = vec{v}A$
$vec{w} = A vec{v}$
$vec{w} = vec{v} A vec{v}$
Both options (a) and (b) are correct.

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

If the matrix

$[[2,8,12],[3,4,0],[8,10,4]]$ is multiplied by the scalar 1/2, what is the result?

$[[4,16,24],[6,8,0],[16,20,8]]$
$[[12,8,2],[0,4,3],[4,10,8]]$
$[[4,6,16],[16,8,20],[24,0,8]]$
$[[1,4,6],[1.5,2,0],[4,5,2]]$

Grade 11 Matrices CCSS: HSA-REI.C.9

Solve the matrix equation.

$[[-1/3, 2],[5,-7]] [[x],[y]] = [[1],[8]]$

$(-27/23, -7/23)$
$(69/37, 23/37)$
$(1,8)$
$(3,1)$

Grade 11 Matrices

For

$A = [[1,3],[4,6]]$ , find

$|A|$ .

-6
6
18
-1

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

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

$[[67,103,89],[109,86,111],[42,99,121]]$
$[[67,86,99],[103,109,121],[89,111,42]]$
$[[42,99,121],[111,86,109],[67,103,89]]$
$[[67,109,42],[103,86,99],[89,111,122]]$

Share/Like This Page

Filter By Grade

Browse Questions

Arithmetic and Number Concepts

Calculus

Function and Algebra Concepts

Absolute Value

Algebraic Expressions

Complex Numbers

Direct and Inverse Variation

Exponents

Functions and Relations

Inequalities

Linear Equations

Literal Equations

Logarithms

Matrices

Nonlinear Equations and Functions

Number Properties

Polynomials and Rational Expressions

Quadratic Equations and Expressions

Radicals

Sequences and Series

Systems of Equations

Vectors

Geometry and Measurement

Mathematical Process

Statistics and Probability Concepts

Trigonometry

Matrices Questions - All Grades