Deck 7: Systems of Equations and Data in Categories

Question 1

If matrix has dimension and matrix has dimension , the dimension of will be .

Answer 1

True

Question 2

Use the graph to find the solution(s) of a system of equations with two unknowns.

A)
B) Infinitely many solutions
C)
D)
E) No solution

Answer 2

Question 3

If the graph of a system of equations results in two parallel lines, then there is/are 2 solution(s) to the system.

Answer 3

False

Question 4

Solve the system of linear equations.

A)
B)
C)
D) Not enough information
E)

Question 5

A solution to a system of equations with 3 unknowns is the point of intersection of 2 lines.

Question 6

When subtracting 2 matrices, the dimensions of all matrices must be the same.

Question 7

If and are matrices, then .

Question 8

The cost of a movie ticket at a local theater is $6.50 per child under 12 years old and $11.75 per adult. On a given day, 3000 people purchased a movie ticket, and the ticket costs collected totaled $26,000. How many children and how many adults purchased a movie ticket that day? (Rounded to the nearest whole number.)

A) 507 children and 2,493 adults
B) 1,762 children and 1,238 adults
C) 1,500 children and 1,500 adults
D) 5,667 children and 8,667 adults
E) 1,951 children and 4,951 adults

Question 9

Solve the system of linear equations.

A)
B)
C)
D) No Solution
E)

Question 10

A matrix is invertible if there exists a matrix such that where also has dimension .

Question 11

A matrix that has no inverse is called singular.

Question 12

The following statement is an example of numerical data: "26 dogs at a given adoption center, tabulated by breeds (Terriers, Hounds, Retrievers)."

Question 13

Solve the system of linear equations. Round to the nearest hundredth.

A) No solution
B)
C)
D)
E)

Question 14

Solve the system of linear equations.

A)
B)
C)
D) No solution.
E)

Question 15

If a system of linear equations of 3 unknowns has infinitely many solutions, then the graph of each equation is identical.

Question 16

When multiplying 3 matrices, the dimensions of all matrices must be the same.

Question 17

To find the inverse of a matrix, we can multiply the matrix by the identity matrix.

Question 18

A chemist mixes two solutions, one containing 8% alcohol and another containing 25% alcohol. How many milliliters of each solution should be mixed to obtain 3 mL of a solution that contains 16% alcohol? Round to the nearest hundredth.

A) 7.24 mL of solution with 8% alcohol and 4.24 mL of solution with 25% alcohol.
B) 0.82 mL of solution with 8% alcohol and 2.18 mL of solution with 25% alcohol.
C) 3.73 mL of solution with 8% alcohol and 2.18 mL of solution with 25% alcohol.
D) 1.59 mL of solution with 8% alcohol and 4.59 mL of solution with 25% alcohol.
E) 1.59 mL of solution with 8% alcohol and 1.41 mL of solution with 25% alcohol.

Question 19

The graph below shows a system of equations. How many solutions exist for this system?

A) 3
B) 0
C) 4
D) 2
E) 1

Question 20

The solution to the system is . (Rounded to the nearest hundredth).

Question 21

Solve the system of linear equations.

A) No solution
B) Infinitely many solutions
C)
D)
E)

Question 22

Find the solution of the system of linear equations described by the following matrix:

A) No solution
B)
C)
D)
E)

Question 23

Which one of the following is the augmented matrix in row-echelon form for the system below?

A)
B)
C)
D)
E)

Question 24

A college conducted a survey of students satisfaction with three academic courses: mathematics, English, and science. The results are tabulated in the data matrix below. How many surveys were completed?

A) 9
B) 48
C) 18
D) 10
E) 20

Question 25

The augmented matrix of a system of linear equations is given below in reduced row-echelon form. What is the solution to this system?

A)
B)
C)
D)
E)

Question 26

Find the solution of the system of linear equations described by the following matrix. Round to nearest hundredth.

A)
B) No solution
C)
D) Infinitely many solutions
E)

Question 27

A college conducted a survey of students satisfaction with three academic courses: mathematics, English, and science. The results are tabulated in the data matrix below. How many students gave a fair rating for these courses?

A) 16
B) 18
C) 14
D) 6
E) 22

Question 28

An investor has $45,000 to invest in three types of accounts. Account A pays 4% annually, Account B pays 6%, and Account C pays 8%. The investor wishes to have a total return of $3000 on the investment, with equal amounts invested in Account B and Account C. How much should be invested in each type of account to satisfy the investor's wishes? Round to the nearest hundredth.

A) Account A = $15,000, Account B = $15,000, Account C = $15,000
B) Account A = $25,000, Account B = $10,00, Account C = $10,000
C) Account A = $5,000, Account B = $20,000, Account C = $20,000
D) There are infinitely many solutions
E) No solution

Question 29

Which one of the following is the augmented matrix for the following system of equations.

A)
B)
C)
D)
E)

Question 30

Find the -entry of the following matrix.

A) 7
B) 4
C) -1
D) 8
E) -7

Question 31

Find the solution of the system of linear equations described by the following matrix:

A) No solution
B) Infinitely many solutions
C)
D)
E)

Question 32

Find the solution of the system of linear equations described by the following matrix. Round to the nearest hundredth.

A)
B)
C) No solution
D)
E) Infinitely many solutions

Question 33

Solve the system of linear equations.

A)
B)
C)
D) No solution
E)

Question 34

Which one of the following is the augmented matrix in row-echelon form for the system below?

A)
B)
C)
D)
E)

Question 35

Solve the system of linear equations.

A)
B)
C) No solution
D)
E)

Question 36

Which one of the following is the dimension of the given matrix?

A)
B)
C)
D)
E)

Question 37

A college conducted a survey of students satisfaction with three academic courses: mathematics, English, and science. The results are tabulated in the data matrix below. How many students rate math as average or above?

A) 9
B) 8
C) 3
D) 11
E) 20

Question 38

Solve the system of linear equations.

A)
B) No solution
C) Infinitely many solutions
D)
E)

Question 39

A chemistry class takes a survey of the number of hours they studied for an exam and the exam score. Of the students who studied less than two hours, 8 students got a score below 60, 3 students got a score between 60 and 80, and 1 above 80. Of the students who studied two to four hours, 3 students got a score below 60, 5 between 60 and 80, and 5 above 80. Of the students who studied more than four hours, 2 student got a score below 60, 1 between 60 and 80, and 4 above 80. Which of the following matrices organizes this data with the columns representing the number of hours students studied and the rows representing the exam score.

A)
B)
C)
D)
E)

Question 40

Which one of the following is the augmented matrix in row-echelon form for the system below?

A)
B)
C)
D)
E)

Question 41

A college conducted a survey of students satisfaction with three academic courses: mathematics, English, and science. The results are tabulated in the data matrix below. What does the -entry represent?

A) The number of students who rated all 3 courses as excellent.
B) The number of students who rated math as an average course.
C) The number of students who rated English as an excellent course.
D) The number of students who completed the survey.
E) The number of students who rated science as a fair course.

Question 42

Which one of the following is the identity matrix?

A)
B)
C)
D)
E)

Question 43

Perform the matrix operation as indicated.

A)
B) Not possible
C)
D)
E)

Question 44

A college conducted a survey of students satisfaction with three academic courses: mathematics, English, and science. The results are tabulated in the data matrix below. Of the students who were surveyed regarding math, what proportion rated math as excellent?

A) 7
B) 0.41
C) 2.57
D) 0.39
E) 18

Question 45

Perform the matrix operation as indicated.

A)
B) Not possible
C)
D)
E)

Question 46

A family sold jewelry during an art festival over a weekend. They sold bracelets, earrings, and necklaces created by 3 different family members. The matrices and tabulate the number of each piece of jewelry sold on Saturday and Sunday. The matrix gives the price per piece of jewelry (in dollars) for each type sold. Find .

A)
B)
C)
D) Not possible
E)

Question 47

Perform the matrix operation as indicated.

A)
B)
C)
D)
E)

Question 48

Perform the matrix operation as indicated.

A)
B)
C)
D)
E) Not possible

Question 49

Perform the matrix operation as indicated.

A)
B) None of the above
C)
D)
E)

Question 50

A college conducted a survey of students satisfaction with three academic courses: mathematics, English, and science. The results are tabulated in the data matrix below. Find the scalar product .

A)
B)
C) None of the above
D)
E)

Question 51

Perform the matrix operation as indicated.

A)
B)
C) Not possible
D)
E)

Question 52

Perform the matrix operation as indicated.

A)
B) Not possible
C)
D)
E)

Question 53

Perform the matrix operation as indicated.

A) Not possible
B)
C)
D)
E)

Question 54

Perform the matrix operation as indicated.

A)
B) Not possible
C)
D)
E)

Question 55

Perform the matrix operation as indicated.

A)
B)
C) Not possible
D)
E)

Question 56

Perform the matrix operation as indicated.

A)
B) Not possible
C)
D)
E)

Question 57

Perform the matrix operation as indicated.

A)
B)
C)
D) Not possible
E)

Question 58

If and are matrices, then when...

A) is the inverse matrix of .
B) is an identity matrix.
C) and are matrices.
D) and are identical matrices.
E) and have the same dimension.

Question 59

Perform the matrix operation as indicated.

A)
B)
C)
D)
E) None of the above

Question 60

Perform the matrix operation as indicated.

A)
B)
C)
D)
E) None of the above

Question 61

Find the inverse matrix of .

A)
B)
C) Not invertible
D)
E)

Question 62

Which one of the following is the variable matrix for the following systems of equations? $\left\{\begin{array}{r}5 x-2 y+6 z=9 \\6 x+2 z=4 \\2 y=3\end{array}\right.$

A) $\left[\begin{array}{lll}x & y & z \\x & y & z \\x & y & z\end{array}\right]$
B) $\left[\begin{array}{l}9 \\4 \\3\end{array}\right]$
C) $\left[\begin{array}{lll}x & y & z\end{array}\right]$
D) $\left[\begin{array}{ccc}5 x & -2 y & 6 z \\6 x & 0 y & 2 z \\0 x & 2 y & 0 z\end{array}\right]$
E) $\left[\begin{array}{l}x \\y \\z\end{array}\right]$

Question 63

Which one of the following is the coefficient matrix for the given system of equations?

A)
B)
C)
D)
E)

Question 64

Find the solution to the given matrix by solving the matrix equation .

A)
B)
C) No solution
D)
E)

Question 65

Two matrices can be subtracted if they have the same...

A) dimension.
B) entries on the first row.
C) number of rows.
D) number of columns.
E) entry.

Question 66

Find the solution to the given matrix by solving the matrix equation .

A) Infinitely many solutions
B) No solution
C)
D)
E)

Question 67

Find the inverse matrix of .

A) Not invertible
B) $\left[\begin{array}{ccc}9 & -3 & 5 \\-3 & 1 & -5\end{array}\right]$
C) $\left[\begin{array}{ccc}1 / 9 & -1 / 3 & 1 / 5 \\-1 / 3 & 1 & -1 / 5\end{array}\right]$
D) $\left[\begin{array}{lll}1 & 0 & 0 \\0 & 1 & 1\end{array}\right]$
E) $\left[\begin{array}{cc}9 & -3 \\-3 & 1 \\5 & -5\end{array}\right]$

Question 68

Find the inverse matrix of .

A) Not invertible
B)
C)
D)
E)

Question 69

Which one of the following is the constant matrix for the following systems of equations? $\left\{\begin{array}{r}4 x-9 y+3 z=8 \\4 x+2 z=3 \\7 y=7\end{array}\right.$

A) $\left[\begin{array}{ccc}4 & -9 & 3 \\4 & 0 & 2 \\0 & 7 & 0\end{array}\right]$
B) $\left[\begin{array}{lll}8 & 3 & 7\end{array}\right]$
C) $\left[\begin{array}{l}8 \\3 \\7\end{array}\right]$
D) $\left[\begin{array}{l}x \\y \\z\end{array}\right]$
E)

Question 70

Find the inverse matrix of .

A)
B)
C) Not invertible
D)
E)

Question 71

Write the system of equations that corresponds to the following augmented matrix:

A)
B)
C)
D)
E)