Linear Systems Using Matrices

Write the system of linear equations into matrix equations 2x-3y=3z-7 4z-2x+3y=12 4y+2z-3x=0

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

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David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• 1.5x+0.5y=78.5
  x+y=87

• 1.5x+0.5y=78.5
  1.5x+0.5y=87

• x+y=78.5
  1.5x+0.5y=87

• x+y=78.5
  x+y=87

A ____________ is a rectangular array of numbers arranged in rows and columns.

Solve the system of equations using Gaussian Elimination.

• (6, 2, 3)

• (3, 2, 6)

• (6, 3, 2)

• (3, 6, 2)

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

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

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

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Find the value of the determinant.

• -29

• -3

• -43

• -25

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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