7. Systems of Equations & Matrices

Introduction to Matrices

Textbook Question
In Exercises 1 - 24, use Gaussian Eliminaion to find the complete solution to each system of equations, or show that none exists.5x + 8y - 6z = 143x + 4y - 2z = 8x + 2y - 2z = 3
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Textbook Question
In Exercises 21–38, 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 problem. See Examples 5 and 9. A cashier has a total of 30 bills, made up of ones, fives, and twenties. The number of twenties is 9 more than the number of ones. The total value of the money is $351. How many of each denomination of bill are there?
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Textbook Question
In Exercises 1–8, write the augmented matrix for each system of linear equations.
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Multiple Choice
Write the equations in standard form, then represent the system using an augmented matrix.
$3x+5y-9=0$
$8x=-4y+3$
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3
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Multiple Choice
Perform the indicated Row Operation.
SWAP $R_1\leftrightarrow R_2$
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Multiple Choice
Perform the indicated Row Operation.
ADD $R_1+2\cdot R_3\rightarrow R_1$
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1
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Multiple Choice
Solve the system of equations by using row operations to write a matrix in REDUCED row-echelon form.
$4x+2y+3z=6$
$x+y+z=3$
$5x+y+2z=5$
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Multiple Choice
Write the system of equations represented by the augmented matrix shown.
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1
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Textbook Question
In Exercises 1–2, perform each matrix row operation and write the new matrix.
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Textbook Question
How many rows and how many columns does this matrix have? What is its dimension? <4x2 Matrix>
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Textbook Question
In Exercises 1 - 4,a. Give the order of each matrix,b. If A = [a_ij], identify a_32 and a_23, or explain why identification is not possible,4 - 7 5- 6 8 - 1(please enclose the values above in a matrix symbol)
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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
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
What is the augmented matrix of the following system? -3x + 5y = 2 6x + 2y = 7
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