7. Systems of Equations & Matrices

Introduction to Matrices

Textbook Question
What is the augmented matrix of the following system? -3x + 5y = 2 6x + 2y = 7
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Textbook Question
In Exercises 3–5, solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
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Textbook Question
Solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.
${\begin{matrix} 3 x_{1} + 5 x_{2} - 8 x_{3} + 5 x_{4} = - 8 \\ x_{1} + 2 x_{2} - 3 x_{3} + x_{4} = - 7 \\ 2 x_{1} + 3 x_{2} - 7 x_{3} + 3 x_{4} = - 11 \\ 4 x_{1} + 8 x_{2} - 10 x_{3} + 7 x_{4} = - 10 \end{matrix}$
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Textbook Question
In Exercises 1–8, write the augmented matrix for each system of linear equations.
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Textbook Question
Use the given row transformation to change each matrix as indicated. See Sample 1. < 2x2 Matrix > ; -4 times row 1 added to row 2
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Textbook Question
In Exercises 1–8, write the augmented matrix for each system of linear equations.
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Textbook Question
Use the given row transformation to change each matrix as indicated. See Sample 1. < 2x2 Matrix > ; -7 times row 1 added to row 2
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Textbook Question
In Exercises 9-12, write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z, for the variables.
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Textbook Question
Use the given row transformation to change each matrix as indicated. See Sample 1. < 3x3 Matrix > ; 2 times row 1 added to row 2
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Textbook Question
In Exercises 9 - 16, find the following matrices: b. A - B
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Textbook Question
Find the dimension of each matrix. Identify any square, column, or row matrices. See the discussion preceding Example 1.
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Textbook Question
In Exercises 9 - 16, find the following matrices: d. - 3A + 2B
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Textbook Question
Use the given row transformation to change each matrix as indicated. See Sample 1. < 3x3 Matrix > ; 4 times row 1 added to row 2
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Textbook Question
In Exercises 9-12, write the system of linear equations represented by the augmented matrix. Use x, y, and z, or, if necessary, w, x, y, and z, for the variables.
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Textbook Question
In Exercises 9 - 16, find the following matrices: a. A + B
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