Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Find the dimensions of the matrix.  a. | 20 ´ 1 | c. | 4 ´
5 | b. | 4 ´ 4 | d. | 5 ´
5 |
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Identify the given matrix element.
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2.
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3.
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4.
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In May, Bradley bought 48 styrofoam balls and decorated them as toy figurines.
In June, he sold 19 figurines. In May, Lupe bought 44 styrofoam balls to decorate, and in June, she
sold 21 figurines. Which matrix represents all of their May purchases and their June sales?
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5.
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State the dimensions of the matrix. Identify the indicated element.  a. | 3 ´ 2, 0 | c. | 2 ´ 3, 4 | b. | 2 ´ 3, –7 | d. | 3 ´ 2,
–7 |
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6.
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How many elements are in an m ´ n
matrix?
a. | m + n | b. |  | c. |  | d. | mn |
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7.
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A matrix contains 60 elements. Which of the following cannot equal the
number of rows of the matrix?
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Find the sum or difference.
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8.
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9.
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10.
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11.
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12.
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Suppose A and B are 2 ´ 5
matrices. Which of the following are the dimensions of the matrix A + B?
a. | 2 ´ 5 | b. | 10 ´ 10 | c. | 7 ´ 1 | d. | 7 ´ 7 |
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Use matrices A, B, and C. Find the sum or difference if
you can.
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13.
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B + A
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14.
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15.
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Find the values of the variables.
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16.
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a. | x = 2, y = 4 | c. | x = 4, y =
2 | b. | x = –1, y = 3 | d. | x = 3, y =
–1 |
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17.
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a. | t = –8, y = 4 | c. | t = –2, y =
6 | b. | t = 6, y = –8 | d. | t = –8, y =
6 |
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18.
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a. | f = 4, k = 4, w = 11 | c. | f = 4, k = –4,
w = 11 or –11 | b. | f = 4, k = 4, w = 11 or
–11 | d. | f = 4,
k = 4, w = 121 or –121 |
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Solve the matrix equation.
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19.
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20.
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21.
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22.
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23.
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24.
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Find the product.
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25.
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26.
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27.
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28.
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Find  . 
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29.
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The Art Department and the Homecoming Committee at a local school are ordering
supplies. The supplies they need are listed in the table. | | Paint (bottles) | Brushes | Paper (reams) | Glue Sticks (boxes) | Tape (rolls) | Art Department | 11 | 12 | 4 | 11 | 4 | Homecoming Committee | 10 | 14 | 7 | 17 | 7 | | | | | | |
A bottle of paint costs
$4, a paint brush costs $2, a ream of colored paper costs $8, a box of glue sticks costs $3, and a
roll of tape costs $2. Find the matrix that represents the total cost of supplies for each
group.
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Determine whether the product is defined or undefined. If defined, give the
dimensions of the product matrix.
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30.
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a. | defined; 3 ´ 3 | c. | defined; 2 ´ 3 | b. | defined; 2 ´
1 | d. | undefined |
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31.
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a. | defined; 2 ´ 2 | c. | defined; 1 ´ 2 | b. | defined; 2 ´
1 | d. | undefined |
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The points represent the vertices of a polygon. Use a matrix to find the
coordinates of the image after the given transformation. Graph the preimage and the image.
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32.
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A(2, 3), B(–1, –4), and C(2, –2); a
translation 1 unit left and 1 unit up 
a. | A¢(1, 4), B¢(1, –1), C¢(–2,
–3)
 | c. | A¢(1, 4), B¢(–2, –3), C¢(1,
–1)
 | b. | A¢(1, 4), B¢(–2, 2), C¢(1,
–1)
 | d. | A¢(1, –1), B¢(–2,
–3), C¢(1, 4)
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33.
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W(2, 0), X(0, 2), Y(–1, 0), and Z(1,
–2); a dilation of 2.5 
a. | W(3, 0), X(0, 3), Y(–1.5, 0), and
Z(1.5, –3) | c. | W(3, 0), X(0, 5),
Y(–1.5, 0), and Z(2.5, –5) | b. | W(2, 0),
X(0, 3), Y(–1, 0), and Z(2.5, –3) | d. | W(5, 0), X(0, 5),
Y(–2.5, 0), and Z(2.5, –5) |
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34.
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A(0, 0), B(–2, 3), and C(2, 1); a reflection across
the y-axis 
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35.
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A(0, 0), B(–1, 3), and C(2, 1); a rotation of
180º 
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Find the coordinates of the image after a reflection in the given
line.
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36.
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 ; y-axis
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37.
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38.
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 -axis
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39.
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Find the coordinates of the image after the given rotation.  
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Which of the following is the multiplicative inverse of the given
matrix?
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40.
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41.
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Evaluate the determinant of the matrix.
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42.
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43.
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44.
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Determine whether the matrix has an inverse. If an inverse exists, find
it.
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45.
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46.
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47.
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Evaluate the determinant.
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48.
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49.
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50.
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Assign each letter and a blank space to a number as shown by the alphabet
table below:
0
= _ | 1 = A | 2 = B | 3 = C | 4 = D | 5 = E | 6 = F | 7 = G | 8 = H | 9 = I | 10 = J | 11 = K | 12 = L | 13 = M | 14 = N | 15 = O | 16 = P | 17 = Q | 18 = R | 19 = S | 20 = T | 21 = U | 22 = V | 23 = W | 24 = X | 25 = Y | 26 = Z | | | | | | | | | |
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51.
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Use  to encode the phrase “FIT AS A
FIDDLE”.
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52.
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The matrix  was used to encode to  . Find  and use it to
decode the matrix. a. | IN BROAD DAYLIGHT | c. | GRIND TO A HALT | b. | RUN LIKE THE WIND | d. | LEAPS AND
BOUNDS |
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53.
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Write the system  as a matrix equation. Then identify the coefficient matrix,
the variable matrix, and the constant matrix.
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54.
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Use an augmented matrix to solve the system  .
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55.
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Write an augmented matrix to represent the system. 
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Use Cramer’s Rule to solve the system.
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56.
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57.
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 . a. | (3, 5, 4) | c. | (–2, –25, 10) | b. | (3, –5,
–4) | d. | (–3,
–5, –4) |
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58.
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Solve the system.
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59.
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a. | (–3, –2, –4) | c. | (3, –2,
–4) | b. | (11, 17, 0) | d. | (–3, 2, 4) |
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60.
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a. | (5, –4, 1) | c. | (5, 4, –1) | b. | (–5, –36,
–13) | d. | (–5,
–4, 1) |
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61.
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a. | no unique solution | c. | (2, 1, 5) | b. | (2, 0, –5) | d. | (–2, 0,
–5) |
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62.
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a. | (19, 14, –2, –7) | c. | (3, 4, –3,
0) | b. | (3, –4, –3, 0) | d. | (–3, 4, 3, –1) |
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63.
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64.
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A gem store sells beads made of amber and quartz. For 4 amber beads and 4 quartz
beads, the cost is $46.00. For 1 amber bead and 3 quartz beads, the cost is $14.50. Find the price of
each type of bead.
a. | amber $10.00, quartz $1.50 | c. | amber $10.25, quartz
$1.75 | b. | amber $9.75, quartz $1.25 | d. | amber $1.50, quartz $10.00 |
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Write the coefficient matrix for the system. Use it to determine whether the
system has a unique solution.
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65.
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a. |  ; yes | c. |  ; no | b. |  ;
no | d. |  ;
yes |
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66.
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a. |  ; no | c. |  ; yes | b. |  ;
yes | d. |  ;
no |
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67.
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Write a system of equations for the augmented matrix  .
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68.
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A graphics designer has a star-shaped figure with vertices whose coordinates are
represented by the matrix below. Her customer wants the figure increased in size by a factor of 1.5.
Find the coordinates of the vertices of the enlargement. 
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Short Answer
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69.
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This table shows data on heating oil use for two years in three adjacent
buildings on Spring Street. Heating Oil Use | Number of
Gallons Used | Address | 2002 | 2003 | | 152 Spring St. | 1215 | 1093 | | 154 Spring St. | 982 | 975 | | 156 Spring St. | 1562 | 1437 | | | |
| a. | Write a matrix H to represent the data. | | b. | Find element  . What does
this element represent? | | |
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70.
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Verify that the matrix has no inverse. 
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71.
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Consider the matrix  | a. | Find and simplify an expression for det
A. | | b. | Use your answer to part (a) to find det A for a = –2. | | |
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72.
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The graph shows the populations of two towns.  | a. | Show the data in a
matrix. | | b. | What does represent? | | |
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73.
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Three friends recorded they amount of time each spent exercising and sleeping
over the course of a week. | | Sleep
(hours) | Exercise
(hours) | | Maria | 56 | 7 | | Validamir | 60 | 5 | | Lee | 63 | 10 | | | |
| a. | Put the information into two matrices. Label each matrix. | | b. | Find the difference
between total hours sleeping and exercising for each person. | | |
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Essay
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74.
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| a. | Write the vertices of
the figure above in a matrix. | | b. | Graph the figure and its image after a reflection in the
x-axis. | | c. | Do any of the vertices of the preimage have the same coordinates as the vertices of the
reflection? Explain. | | d. | Give the coordinates of a point of the preimage that is also a point of the
reflection. | | |
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75.
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The following tables show car and SUV sales for a dealership in 1990 and 2000.
The months shown represent the end of each quarter. Sales in
1990
| | March | June | September | December | SUVs | 60 | 33 | 26 | 77 | Cars | 128 | 201 | 179 | 114 | | | | | |
Sales in 2000
| | March | June | September | December | SUVs | 110 | 66 | 80 | 118 | Cars | 122 | 188 | 176 | 99 | | | | | |
| a. | Organize the information into two 2 x 4 matrices, A (1990) and B
(2000). | | b. | Calculate the matrix that shows the change in sales from 1990 to 2000. | | c. | For which type of
vehicle did sales increase? Explain. | | |
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76.
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Mr. Gabrielli teaches French and Spanish. This chart shows the mean scores on
the vocabulary sections and comprehension sections of tests for two different classes of each
language. Mean
Scores | | | | Class 1 | Class 2 | Vocabulary | French
Spanish | 32
41 | 39
35 | Comprehension | French
Spanish | 35
39 | 42
43 | | | | | |
| a. | Write matrices for the vocabulary (V) scores and the comprehension
(C) scores. | | b. | Write the matrix for the combined scores, V + C. | | c. | Which class had the higher combined test
scores, and for which language? | | |
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Other
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77.
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What does the expression  represent if A is a matrix? If
 exists, what can you say about the dimensions of A? Explain.
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78.
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Write a system of three equations that has a unique solution of (1, 2,
3).
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79.
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The matrix  has no inverse. Explain how you can determine the value of
x. Then find x.
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80.
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Determine whether the following statement is always, sometimes or
never true.Explain your answer.
Given two different n x n matrices A
and B, AB = BA.
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81.
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A triangle has vertices A(1, 1), B(3, 2), and C(-2,
4). | a. | Transform
the triangle by multiplying  . | | b. | Graph the preimage and image. | | c. | Describe the
transformation. | | |
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