Unit test on Matrices and Determinants
(The answers are in red.)
Use the following matrix for questions 1 and 2:
1. Write the dimensions of matrix A. Matix A is a 3 x 2 matrix
2. Write the element in row three, column 2 . 4
3. Write the zero matrix 02x3
4. Find x, y, and z:
x = y; y -1 = 6, so y = 6 + 1 or 7; 3z = 9, so z = 9/3 or 3.
(7, 7, 3)
5. Perform the indicated operation
6. Solve for the matrix X2X 2:
7. Write the identify matrix I2x2.
8. Which of the following cannot be multiplied?
The dimensions are given by the number of rows x the number of columns.
a. a 1x1 times a 1 x 1 b. a 1 x 1 times a 1 x 2 c. a 2 x 1 times a 2 x 2
d. a 1 x 2 times a 2 x 2 e. a 2 x 2 times a 2 x 1
The answer is c. The column of the first matrix must be the same as the row of the second matric.
11. Multiply the matrix by the scalar.
Use the given communication network to answer the following questions:
12. Write the communication matrix.
14. Which computer(s) can send data directly to the LEAST number of computers? 4
15. Which computer(s) can receive data directly from the greatest number of computers? 1
16. Find the determinant of
Evaluate the determinant of the following matrices.
19. If A =
20. Use inverse matrix properties to solve for x and y. 20. x = _______; y = ______
3x + y = 7
2x - 3y = 1
21. Check your answers for number 20.
22 - 23. Use Cramer's Rule to evaluate the following system:
22. x = _____; 23. y = _____; z = _____
2x - 3y + 5z = 3
4x - y + z = 1
3x - 2y + 3x = 4
24 - 25. Use determinants to find the area of the triangle shown below.
24. base = ______ 25. height = _____
26 - 28. Find the atomic weight of each chemical element in the chart below.
*Hint: use Cramer's Rule.
Compound Symbol Atomic
Water H2O 10
Carbon Dioxide CO2 22
Furan C4H4O 36
26. Hydrogen _______ 27. Oxygen 28. Carbon ______
BONUS for all students: Use what you know about matrices to solve the following real life problem.
(hint: Use the formula: (X1x2 )(Y1x3 ); let Matrix X = the number of loaves and
Matrix Y = the dry ingredients.)
A bakery's recipe for regular white bread and French bread include the following proportions for the dry ingredients (in grams per loaf.)
Flour Sugar Salt
Regular 434 14 6
French 267 6 6
If the bakery pans to bake 150 loaves of regular bread and 60 loaves of French bread , write a matrix for the total dry ingredients. How much of each dry ingredient is needed?
Expansion to minors: For Advanced Algebra II students only.
Expand the matrix to minors around the given row or column to find the determinants.