Algebra 2 Practice Test on Matrices

Algebra 2 Practice Test on Matrices

1. Find A + B.

A =

B =

Perform the indicated matrix operation, if possible. 2.

3.

4. The Revenue and Expenses for two pet shops for a 2-month period are shown below. Write a matrix that shows the monthly profit for each pet shop. Which pet shop has the higher overall profit during the 2-month period?

Revenue ($) Pets A Pets B

Expenses ($) Pets A Pets B

June

June

July

July

Solve the matrix equation for x and y. 5. 6.

7. A magic square consists of numbers in a square grid for which the sum of the numbers in each column, row, and diagonal is the same number. An example of a magic square is shown below.

The magic square can be represented by the matrix

a. Find 3A.

b. Find

where

c. Find

and

where

d. Do the resulting matrices represent magic squares?

Perform the matrix operations, if possible. 8.

9.

10.

____ 11. Given A = a.

b.

and B =

, find AB. c.

d.

Is the product of the following pair of matrices defined? Write Yes or No. If yes, give the dimensions of the product matrix. 12. 13. Use the matrices K, L, M, and N to evaluate each matrix expression. If the operation cannot be performed, write undefined.

14. 4M

15. 7K ? 2L

16. A company stocks items A, B, and C at each of its two stores. Use matrix multiplication to determine the value of the inventory at each store.

Evaluate the determinant of the matrix. 17.

18.

19.

20. A real estate agent is writing a listing for a triangular piece of land. She has to include the number of square feet for the property and has to calculate it from a plot that shows the following information: one corner of the plot is 140 feet south and 148 feet east from the upper vertex of the plot, the other corner is 20 feet south and 252 feet east from the upper vertex of the plot. Use matrices to find the area of the piece of land.

Find the area of the triangle. 21.

Use Cramer's Rule to solve for y. 22.

Find the coefficient matrix and evaluate its determinant. 23.

Use Cramer's Rule to solve the linear system. 24.

Find the inverse of the matrix. 25.

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