Review Exercise Set 20 PDF Exercise 1: Use Gaussian elimination

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Review Exercise Set 20

Exercise 1: Use Gaussian elimination to find the solution for the given system of equations. 3x + y - z = 1 Perform row operations to reduce the matrix ...

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Answer: 8. In Exercises 9–12 solve the linear system by Gaussian elimination. in the general solution of the linear system with augmented matrix B?

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Review Exercise Set 20

Exercise 1: Use Gaussian elimination to find the solution for the given system of equations.

3x + y

- z = 1 x - y + z = -3

2x + y + z = 0

Exercise 2: Use Gaussian elimination to find the solution for the given system of equations.

2x + 5y = 9

x + 2y - z = 3 -3x - 4y + 7z = 1

Exercise 3: The circle given by the equation x

2 + y 2 + ax + by + c = 0 passes through the points (-2, 0), (-1, 7), and (5, -1). Find a, b, and c.

Review Exercise Set 20 Answer Key

Exercise 1: Use Gaussian elimination to find the solution for the given system of equations.

3x + y

- z = 1 x - y + z = -3

2x + y + z = 0

Setup the augmented matrix

Perform row operations to reduce the matrix

Exercise 1 (Continued):

The solution set (x, y, z) is

17 3,,24 4

Exercise 2: Use Gaussian elimination to find the solution for the given system of equations.

2x + 5y = 9

x + 2y - z = 3 -3x - 4y + 7z = 1

Setup the augmented matrix

Perform row operations to reduce the matrix

Exercise 2 (Continued):

0 4 so this system is inconsistent and has no solution.

Exercise 3: The circle given by the equation x

2 + y 2 + ax + by + c = 0 passes through the points (-2, 0), (-1, 7), and (5, -1). Find a, b, and c. Substitute the given points into the equation to find the system of equations x 2 + y 2 + ax + by + c = 0 (-2) 2 + (0) 2 + a(-2) + b(0) + c = 0

4 - 2a + c = 0

-2a + c = -4 x 2 + y 2 + ax + by + c = 0 (-1) 2 + (7) 2 + a(-1) + b(7) + c = 0

1 + 49 - a + 7b + c = 0

-a + 7b + c = -50 x 2 + y 2 + ax + by + c = 0 (5) 2 + (-1) 2 + a(5) + b(-1) + c = 0

25 + 1 + 5a - b + c = 0

5a - b + c = -26

-2a + c = -4 -a + 7b + c = -50

5a - b + c = -26

Setup the augmented matrix

Exercise 3 (Continued):

Perform row operations to reduce the matrix

Exercise 3 (Continued):

The solution set (a, b, c) is (-4, -6, -12)

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[PDF] Review Exercise Set 20 Exercise 1: Use Gaussian elimination

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Review Exercise Set 20

Exercise Set 1.4

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Exercise Set 1.2

Exercise Set 5.1

Review Exercise Set 20

3x + y

2x + y + z = 0

2x + 5y = 9

Exercise 3: The circle given by the equation x

Review Exercise Set 20 Answer Key

3x + y

2x + y + z = 0

Setup the augmented matrix

Perform row operations to reduce the matrix

Exercise 1 (Continued):

The solution set (x, y, z) is

17 3,,24 4

2x + 5y = 9

Setup the augmented matrix

Perform row operations to reduce the matrix

Exercise 2 (Continued):

0 4 so this system is inconsistent and has no solution.

Exercise 3: The circle given by the equation x

4 - 2a + c = 0

1 + 49 - a + 7b + c = 0

25 + 1 + 5a - b + c = 0

5a - b + c = -26

5a - b + c = -26

Setup the augmented matrix

Exercise 3 (Continued):

Perform row operations to reduce the matrix

Exercise 3 (Continued):

The solution set (a, b, c) is (-4, -6, -12)