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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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Use matrices to find the system of equations (if
possible). Use Gaussian elimination with
back-substitution or Gauss-Jordan
elimination.
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3.
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Fill in the blank using elementary row operations
to form a row-equivalent matrix.
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4.
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An augmented matrix that represents a system of
linear equations (in variables x, y, and z) has been reduced using Gauss-Jordan
elimination. Write the solution represented by the augmented matrix.
a. | x = 0, y = 0, z =
0 | b. | x = –5x, y =
–4y, z = –3z | c. | x =
–5, y = –3, z = –4 | d. | x = 5, y = 3, z = 4 | e. | x = –5, y = 0, z =
0 |
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5.
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Use matrices to solve the system of equations (if
possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
a. | x = 5, y =
–1 | b. | x = 1, y =
–5 | c. | x = –1, y =
5 | d. | x = 5, y = 1 | e. | no solution |
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6.
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Use matrices to solve the system of equations (if
possible). Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
a. | x = –5, y = –3, z =
2 | b. | x = 3, y = –5, z =
–2 | c. | x = 5, y = –3, z =
2 | d. | no solution | e. | x = 5, y = 3, z =
2 |
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7.
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Find  .
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8.
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If possible, find  and state the
order of the result.
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9.
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Write the system of linear equations as a matrix
equation,  .
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10.
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Use the inverse formula 
to find the inverse of the  matrix (if it exists).
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11.
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Use the inverse formula  to find the inverse of the  matrix (if it
exists).
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12.
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Use the inverse formula 
to find the inverse of the  matrix (if it exists).
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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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Use the matrix capabilities of a graphing utility
to find the determinant of the matrix
 .
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15.
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Evaluate the determinant of the matrix below to
determine which of the following makes the equation true.
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16.
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Use Crammer’s Rule to solve (if possible) the
system of equations.
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17.
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Find a value of such that the triangle with the
given vertices has an area of 6 square units.
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18.
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Use determinants to find the area of a triangle
with given vertices and confirm your answer by plotting the points in a coordinate plane and using
the formula
Area =  .
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19.
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Use a determinant and the given vertices of a
triangle to find the area of the triangle.
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20.
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Use a determinant and the given vertices of a
triangle to find the area of the triangle.
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