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1.
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Select the augmented matrix for the system of
linear equations.
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2.
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Fill in the blank(s) using elementary row
operations to form a row-equivalent matrix.
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3.
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Write the augmented matrix for the system of linear
equations.
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4.
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Fill in the blank using elementary row operations
to form a row-equivalent matrix.
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5.
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Determine whether the two systems of linear
equations yield the same solutions. If so, find the solutions using matrices.
a. | x = –3, y = –6, z =
2 | b. | The systems yield different
solutions. | c. | x = 3,
y = 2, z = –3 | d. | x = 3,
y = 6, z = 2 | e. | x =
–6, y = 2, z = –3 |
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6.
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Find  .
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7.
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Evaluate the expression.
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8.
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Evaluate the expression.
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9.
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Solve for X in the equation given.
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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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Use the matrix capabilities of a graphing utility
to solve the following system of linear equations:
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13.
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Find all the cofactors of the
matrix.
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14.
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Find the determinant of the matrix by the method of
expansion by cofactors. Expand using the column 2.
a. | –423 | b. | 423 | c. | –421 | d. | –422 | e. | –424 |
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15.
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Find  .
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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 a graphing utility and Cramer’s Rule to
solve (if possible) the system of equations.
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18.
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Use Crammer’s Rule to solve (if possible) the
system of equations.
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19.
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Find a value of such that the triangle with the
given vertices has an area of 4 square units.
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20.
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Use a determinant to determine whether the points
 and  are
collinear.
a. |  ; therefore, the points are
not collinear. | b. |  ;
therefore, the points are collinear. |
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