7. Systems of Equations & Matrices

Introduction to Matrices

7. Systems of Equations & Matrices

Introduction to Matrices

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Introduction to Matrices

Performing Row Operations on Matrices

Solving Systems of Equations - Matrices (Row-Echelon Form)

Solving Systems of Equations - Matrices (Reduced Row-Echelon Form)

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Multiplying Matrices - Example 2

Gaussian Elimination with Back Substitution

Mario's Math Tutoring

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Solve linear systems using Gaussian elimination with back substitution

06:33

Solve linear systems using Gaussian elimination with back substitution

Gaussian Elimination & Row Echelon Form

The Organic Chemistry Tutor

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❤︎² Gaussian Elimination.. How? (mathbff)

09:54

❤︎² Gaussian Elimination.. How? (mathbff)

Using Gauss-Jordan to Solve a System of Three Linear Equations - Example 2

Inverse Matrix Using Gauss-Jordan / Row Reduction, Example 1

Inverse Matrix Using Gauss-Jordan / Row Reduction, Example 2

patrickJMT

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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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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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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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Textbook Question

In Exercises 1–8, write the augmented matrix for each system of linear equations.

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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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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

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

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 4 1 5 9 A = B = 3 2 0 7

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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 4 1 5 9 A = B = 3 2 0 7

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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 3 1 1 2 - 3 6 A = B = - 1 2 5 - 3 1 - 4

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Textbook Question

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B 3 1 1 2 - 3 6 A = B = - 1 2 5 - 3 1 - 4

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Textbook Question

In Exercises 9 - 16, find the following matrices: c. - 4A 3 1 1 2 - 3 6 A = B = - 1 2 5 - 3 1 - 4

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Textbook Question

Write the augmented matrix for each system and give its dimension. Do not solve. 2x + y + z - 3 = 0 3x - 4y + 2z + 7 = 0 x + y + z - 2 = 0

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Textbook Question

In Exercises 13–18, perform each matrix row operation and write the new matrix.

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Textbook Question

Write the augmented matrix for each system and give its dimension. Do not solve. 4x - 2y + 3z - 4 = 0 3x + 5y + z - 7 = 0 5x - y + 4z - 7 = 0

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Textbook Question

In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. A+D

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Textbook Question

In Exercises 9 - 16, find the following matrices: a. A + B A = [6 2 - 3], B = [4 - 2 3]

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Textbook Question

In Exercises 9 - 16, find the following matrices: c. - 4A A = [6 2 - 3], B = [4 - 2 3]

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Textbook Question

In Exercises 13–18, perform each matrix row operation and write the new matrix.

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Textbook Question

Write the system of equations associated with each augmented matrix . Do not solve. <4x3 Matrix>

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Textbook Question

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B 2 - 10 - 2 6 10 - 2 A = 14 12 10 B = 0 - 12 - 4 4 - 2 2 - 5 2 - 2

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Textbook Question

In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. D-A

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Textbook Question

In Exercises 13–18, perform each matrix row operation and write the new matrix.

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Textbook Question

Write the system of equations associated with each augmented matrix . Do not solve. <4x3 Matrix>

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Textbook Question

In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. 3A+2D

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Textbook Question

In Exercises 19–20, a few steps in the process of simplifying the given matrix to row-echelon form, with 1s down the diagonal from upper left to lower right, and 0s below the 1s, are shown. Fill in the missing numbers in the steps that are shown.

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Textbook Question

Write the system of equations associated with each augmented matrix . Do not solve.

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Textbook Question

Find the values of the variables for which each statement is true, if possible. See Examples 1 and 2. =

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Textbook Question

In Exercises 17 - 26, let - 3 - 7 - 5 - 1 A = 2 - 9 and B = 0 0 5 0 3 - 4 Solve each matrix equation for X. 2X + A = B

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Textbook Question

In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. -5(A+D)

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Textbook Question

Use the Gauss-Jordan method to solve each system of equations. For systems in two variables with infinitely many solutions, write the solution with y arbitrary. For systems in three variables with infinitely many solutions, write the solution set with z arbitrary. See Examples 1-4. x + y = 5 x - y = -1

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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

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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

In Exercises 14–27, perform the indicated matrix operations given that and D are defined as follows. If an operation is not defined, state the reason. BD

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Textbook Question

Solve each system, using the method indicated. 5x + 2y = -10 3x - 5y = -6 (Gauss-Jordan)

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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

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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

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Textbook Question

Solve each system, using the method indicated. 3x + y = -7 x - y = -5 (Gaussian elimination)

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Textbook Question

Solve for X in the matrix equation 3X+A = B where

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Textbook Question

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Textbook Question

Solve each system, using the method indicated. x - z = -3 y + z = 6 2x - 3z = -9 (Gauss-Jordan)

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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

In Exercises 27 - 36, find (if possible) the following matrices: a. AB b. BA 1 2 A = [1 2 3 4], B = 3 4

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Textbook Question

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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

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

In Exercises 27 - 36, find (if possible) the following matrices: a. AB b. BA 4 2 2 3 4 A = 6 1 B = 3 5 - 1 - 2 0

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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

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

Find the quadratic function f(x) = ax² + bx + c for which ƒ( − 2) = −4, ƒ(1) = 2, and f(2) = 0.

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Textbook Question

Find each sum or difference, if possible. See Examples 2 and 3. <1x4 Matrix> - <1x4 Matrix>

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Textbook Question

Find the cubic function f(x) = ax³ + bx² + cx + d for which ƒ( − 1) = 0, ƒ(1) = 2, ƒ(2) = 3, and ƒ(3) = 12.

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Textbook Question

Solve the system: (Hint: Let A = ln w, B = ln x, C = ln y, and D = ln z. Solve the system for A, B, C, and D. Then use the logarithmic equations to find w, x, y, and z.)

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Textbook Question

In Exercises 37 - 44, perform the indicated matrix operations given that A, B and C are defined as follows. If an operation is not defined, state the reason. 4 0 5 1 1 - 1 A = - 3 5 B = C = 0 1 - 2 - 2 - 1 1 A(BC)

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Textbook Question

Let A = and B = . Find each of the following. See Examples 2 –4. (3/2)B

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Textbook Question

Find each product, if possible. See Examples 5–7. <4x2 Matrix>

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Textbook Question

Find the values of the variables for which each statement is true, if possible. [2x2 matrix] = [2x2 matrix]

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7. Systems of Equations & Matrices

Introduction to Matrices

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