Systems of Linear Equations and Matrices

Solve the system of equations using Gaussian Elimination.

25x + 60y + 80z = 510

40x + 20y + 15z = 325

60x + 90y + 100z = 840

• (6, 2, 3)

• (3, 2, 6)

• (6, 3, 2)

• (3, 6, 2)

Solve the system of linear equations.

4x + 3y – z = –10

–2x – y + 5z = 24

–3x + 2y – 6z = –11

• x = –3, y = 2, z = 4

• x = –2, y = 2, z = 4

• x = 2, y = 2, z = 4

• x = 3, y = 2, z = 4 x = 3, y = 2, z = 4

Write the augmented matrix for the system of linear equations.

2w – 3x + 4z = –12

–3w + 6y – 9z = 7

–x + 4y – 5z = 2

w + 6x + 4y = –9

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Which of the following matrices is in row-echelon form?

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Find the inverse of 

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Which of the following shows the system of equations using a matrix equation?

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Solve the systems of equations by using matrix equations.

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Find the value of the determinant.

• -29

• -3

• -43

• -25

Use an inverse matrix to solve the system of equations.

7x − 9y = 13

−4x + 5y = −8

• x = -7, y = -4

• x = 7, y = 4

• x = -123, y = 157

• x = 123, y = -157

Bonny has 21 coins consisting of quarters, dimes, and nickels. The total value of the coins is $4.05. She has twice as many quarters as dimes and nickels combined. Write a system of equations that represent the situation.

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