PC Chapter 6 Review (Matrices)

Use the elimination method to solve the system of equations.

2x - 4y = 9

3x + 4y = 1

Answer explanation

Add the equations to eliminate the y variable.

Find A + B

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Answer explanation

Add the corresponding elements

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

Answer explanation

The leading coefficient in Equation 1 is not 1, so replace Equation 1 with (Equation 1 + Equation 2).

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

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Answer explanation

A matrix is in row-echelon form if rows consisting entirely of zeros appear at the bottom of the matrix, the first entry in any row with nonzero entries is 1, and for two successive rows with nonzero entries, the leading 1 in the higher row is farther to the left than the leading 1 in the lower row.

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

2x + y = 5

x - y = 1

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Answer explanation

For the square matrix, write the coefficients in the order in which they occur.

Find the value of the determinant

Mathematical Equivalence

OFF

Answer explanation

Find the minor of each of the elements in the first row.

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

Answer explanation

Use the formula for the inverse of a 2x2 matrix

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. Find the inverse matrix for the system of equations.

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Answer explanation

Create a matrix and augment it with the Identity matrix, then complete RREF

Mathematical Equivalence

ON

Answer explanation

Rewrite the expression as partial fractions with constant numerators, and denominators that are the linear factors of the original denominator.

Answer explanation

Use polynomial division to rewrite the expression as a proper rational expression.