Multiple Choice Identify the
choice that best completes the statement or answers the question.
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1.
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Write the system of linear equations represented by
the augmented matrix. (Use variables x, y, z, and w.)
![mc001-1.jpg](chapter_8_pre_test_files/mc001-1.jpg)
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2.
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Identify the elementary row operation being
performed to obtain the new row-equivalent matrix.
Original Matrix | New
Row-Equivalent Matrix | | | | |
a. | Add –2 times R2 to
R1. | b. | Add 2 times
R2 to R1. | c. | Add –2 times
R1 to R2. | d. | Add 2 times
R1 to R2. | e. | Add 2 times
R1 to R1. |
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3.
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Write the system of linear equations represented by
the augmented matrix. Then use back-substitution to solve. (Use variables x, y, and
z.)
![mc003-1.jpg](chapter_8_pre_test_files/mc003-1.jpg)
a. | x = 83, y = –5, z =
–4 | b. | x = –2, y = –1, z =
3 | c. | x = –1, y = 2, z =
–3 | d. | x = –1, y = –2, z =
3 | e. | x = 2, y = 3, z =
1 |
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4.
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Determine whether the two systems of linear
equations yield the same solutions. If so, find the solutions using matrices.
![mc004-1.jpg](chapter_8_pre_test_files/mc004-1.jpg)
![mc004-2.jpg](chapter_8_pre_test_files/mc004-2.jpg)
a. | The systems yield different
solutions. | b. | x = 3,
y = 6, z = 2 | c. | x =
–6, y = 2, z = –3 | d. | x =
–3, y = –6, z = 2 | e. | x = 3,
y = 2, z = –3 |
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5.
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The currents in an electrical network are given by
the solutions of the system
![mc005-1.jpg](chapter_8_pre_test_files/mc005-1.jpg) where I1, I2,
and I3 are measured in amperes. Solve the system of equations using
matrices.
a. | I1 = 3, I2 = 5,
I3 = 8 | b. | I1 = 5, I2 = 3, I3 =
8 | c. | no solution | d. | I1 = 5, I2 = 8, I3 =
3 | e. | I1 = 3, I2 = 5,
I3 = 9 |
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6.
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Evaluate the expression.
![mc006-1.jpg](chapter_8_pre_test_files/mc006-1.jpg)
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7.
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Evaluate the expression.
![mc007-1.jpg](chapter_8_pre_test_files/mc007-1.jpg)
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8.
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If possible, find AB.
![mc008-1.jpg](chapter_8_pre_test_files/mc008-1.jpg)
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9.
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Use the matrix capabilities of a graphing utility
to find AB, if possible.
![mc009-1.jpg](chapter_8_pre_test_files/mc009-1.jpg)
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10.
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Find the inverse of the matrix .
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11.
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Find the inverse of the matrix
(if it exists).
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12.
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Solve the system of linear
equations
using the inverse matrix .
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13.
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Solve the system of linear
equations
using the inverse matrix
.
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14.
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Solve the system of linear
equations
using an inverse
matrix.
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15.
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Find the determinant of .
a. | 7 | b. | –4 | c. | ![mc015-2.jpg](chapter_8_pre_test_files/mc015-2.jpg) | d. | 8 | e. | –3 |
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16.
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Use the matrix capabilities of a graphing utility
to find the determinant of the matrix
.
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17.
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Use the matrix capabilities of a graphing utility
to find the determinant of the matrix
.
a. | –384 | b. | –32 | c. | –64 | d. | –48 | e. | 128 |
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18.
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Given , find .
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19.
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Solve for x given the following equation
involving a determinant.
![mc019-1.jpg](chapter_8_pre_test_files/mc019-1.jpg)
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20.
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Use a determinant to find y such that , and are collinear.
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