Algebra 2 Matrices Review
Algebra 2 Matrices Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find [pic].
[pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Evaluate the determinant of the matrix.
____ 2. [pic]
|a. |30 |b. |–50 |c. |–30 |d. |–40 |
____ 3. A matrix contains 48 elements. Which of the following cannot equal the number of rows of the matrix?
|a. |18 |b. |16 |c. |8 |d. |24 |
Use Cramer’s Rule to solve the system.
____ 4. [pic]
|a. |[pic] |b. |no solution |c. |[pic] |d. |[pic] |
Identify the given matrix element.
____ 5. [pic]
[pic]
|a. |9 |b. |–7 |c. |2 |d. |–6 |
____ 6. [pic]
[pic]
|a. |–1 |b. |2 |c. |0 |d. |–5 |
Solve the system.
____ 7. [pic]
|a. |[pic] |b. |[pic] |c. |[pic] |d. |no solution |
____ 8. [pic]
|a. |(1, 1, 0) |c. |(1, –1, –1) |
|b. |(6, 5, 0) |d. |(–1, 1, 0) |
Find the product.
____ 9. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 10. [pic]
|a. |[pic] |c. |[pic] |
|b. |[2] |d. |[pic] |
____ 11. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Use matrices A, B, and C. Find the sum or difference if you can.
[pic]
____ 12. C + A
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |not possible |
____ 13. [pic]
|a. |not possible |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 14. State the dimensions of the matrix. Identify the indicated element.
[pic]
|a. |3 × 2, 5 |c. |2 × 3, –7 |
|b. |2 × 3, 1 |d. |3 × 2, –7 |
Solve the matrix equation.
____ 15. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 16. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 17. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Find the values of the variables.
____ 18. [pic]
|a. |f = –1, k = 7, w = 9 or –9 |c. |f = –1, k = –7, w = 81 or –81 |
|b. |f = –1, k = –7, w = 9 |d. |f = –1, k = –7, w = 9 or –9 |
____ 19. [pic]
|a. |t = 1, y = –1 |c. |t = –1, y = 2 |
|b. |t = –11, y = 1 |d. |t = –1, y = 1 |
Evaluate the determinant.
____ 20. [pic]
|a. |–120 |b. |20 |c. |120 |d. |–20 |
Find the sum or difference.
____ 21. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 22. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 23. Suppose A and B are 2 × 1 matrices. Which of the following are the dimensions of the matrix A + B?
|a. |2 × 1 |b. |3 × 1 |c. |2 × 2 |d. |3 × 3 |
Algebra 2 Matrices Review
Answer Section
MULTIPLE CHOICE
1. ANS: D PTS: 1 DIF: L2 REF: 4-3 Matrix Multiplication
OBJ: 4-3.1 Multiplying a Matrix by a Scalar STA: MS AII 7d
TOP: 4-3 Example 2 KEY: scalar multiplication | matrix subtraction | matrix
2. ANS: C PTS: 1 DIF: L2
REF: 4-6 3 x 3 Matrices, Determinants, and Inverses
OBJ: 4-6.1 Evaluating Determinants of 3 x 3 Matrices STA: MS AII 7b
TOP: 4-6 Example 1 KEY: determinant | 3 x 3 matrix | matrix
3. ANS: A PTS: 1 DIF: L4 REF: 4-1 Organizing Data Into Matrices
OBJ: 4-1.1 Identifying Matrices STA: MS AII 7a
KEY: matrix | dimensions of a matrix | matrix element
4. ANS: D PTS: 1 DIF: L3
REF: 4-8 Augmented Matrices and Systems
OBJ: 4-8.1 Solving Systems Using Cramer's Rule STA: MS AII 2a
TOP: 4-8 Example 1 KEY: Cramer's Rule | systems and matrices | 2 x 2 matrix
5. ANS: D PTS: 1 DIF: L2 REF: 4-1 Organizing Data Into Matrices
OBJ: 4-1.1 Identifying Matrices STA: MS AII 7a TOP: 4-1 Example 2
KEY: matrix | matrix element
6. ANS: D PTS: 1 DIF: L2 REF: 4-1 Organizing Data Into Matrices
OBJ: 4-1.1 Identifying Matrices STA: MS AII 7a TOP: 4-1 Example 2
KEY: matrix | matrix element
7. ANS: C PTS: 1 DIF: L2 REF: 4-7 Inverse Matrices and Systems
OBJ: 4-7.1 Solving Systems of Equations Using Inverse Matrices
STA: MS AII 2a TOP: 4-7 Example 2
KEY: systems and matrices | 2 x 2 matrix | matrix equation
8. ANS: A PTS: 1 DIF: L2
REF: 4-8 Augmented Matrices and Systems
OBJ: 4-8.1 Solving Systems Using Cramer's Rule STA: MS AII 2a
TOP: 4-8 Example 2 KEY: systems and matrices | 3 x 3 matrix | Cramer's Rule
9. ANS: D PTS: 1 DIF: L2 REF: 4-3 Matrix Multiplication
OBJ: 4-3.2 Multiplying Matrices STA: MS AII 7d TOP: 4-3 Example 4
KEY: matrix multiplication | matrix
10. ANS: B PTS: 1 DIF: L3 REF: 4-3 Matrix Multiplication
OBJ: 4-3.2 Multiplying Matrices STA: MS AII 7d TOP: 4-3 Example 4
KEY: matrix multiplication | matrix
11. ANS: B PTS: 1 DIF: L2 REF: 4-3 Matrix Multiplication
OBJ: 4-3.1 Multiplying a Matrix by a Scalar STA: MS AII 7d
TOP: 4-3 Example 1 KEY: scalar | scalar multiplication | matrix
12. ANS: D PTS: 1 DIF: L3
REF: 4-2 Adding and Subtracting Matrices
OBJ: 4-2.1 Adding and Subtracting Matrices STA: MS AII 7c | MS AII 7d
TOP: 4-2 Example 1
KEY: matrix addition | dimensions of a matrix | matrix subtraction
13. ANS: B PTS: 1 DIF: L2
REF: 4-2 Adding and Subtracting Matrices
OBJ: 4-2.1 Adding and Subtracting Matrices STA: MS AII 7c | MS AII 7d
TOP: 4-2 Example 1
KEY: matrix subtraction | dimensions of a matrix | matrix addition
14. ANS: D PTS: 1 DIF: L3 REF: 4-1 Organizing Data Into Matrices
OBJ: 4-1.1 Identifying Matrices STA: MS AII 7a TOP: 4-1 Example 1
KEY: matrix | dimensions of a matrix | matrix element
15. ANS: B PTS: 1 DIF: L2
REF: 4-5 2 x 2 Matrices, Determinants, and Inverses
OBJ: 4-5.2 Using Inverse Matrices to Solve Equations STA: MS AII 7b
TOP: 4-5 Example 4
KEY: inverse matrices | matrix | multiplicative inverse of a matrix
16. ANS: D PTS: 1 DIF: L2 REF: 4-3 Matrix Multiplication
OBJ: 4-3.1 Multiplying a Matrix by a Scalar STA: MS AII 7d
TOP: 4-3 Example 3 KEY: scalar | scalar multiplication | matrix | matrix equation
17. ANS: D PTS: 1 DIF: L2
REF: 4-2 Adding and Subtracting Matrices OBJ: 4-2.2 Solving Matrix Equations
STA: MS AII 7c | MS AII 7d TOP: 4-2 Example 4
KEY: matrix equation
18. ANS: D PTS: 1 DIF: L4
REF: 4-2 Adding and Subtracting Matrices OBJ: 4-2.2 Solving Matrix Equations
STA: MS AII 7c | MS AII 7d TOP: 4-2 Example 6
KEY: matrix | matrix equation | matrix element
19. ANS: D PTS: 1 DIF: L2
REF: 4-2 Adding and Subtracting Matrices OBJ: 4-2.2 Solving Matrix Equations
STA: MS AII 7c | MS AII 7d TOP: 4-2 Example 6
KEY: matrix | matrix equation | matrix element
20. ANS: B PTS: 1 DIF: L3
REF: 4-5 2 x 2 Matrices, Determinants, and Inverses
OBJ: 4-5.1 Evaluating Determinants of 2 x 2 Matrices STA: MS AII 7b
KEY: determinant | 2 x 2 matrix | matrix
21. ANS: D PTS: 1 DIF: L2
REF: 4-2 Adding and Subtracting Matrices
OBJ: 4-2.1 Adding and Subtracting Matrices STA: MS AII 7c | MS AII 7d
TOP: 4-2 Example 2 KEY: matrix addition | matrix
22. ANS: B PTS: 1 DIF: L2
REF: 4-2 Adding and Subtracting Matrices
OBJ: 4-2.1 Adding and Subtracting Matrices STA: MS AII 7c | MS AII 7d
TOP: 4-2 Example 3 KEY: matrix subtraction | matrix
23. ANS: A PTS: 1 DIF: L3
REF: 4-2 Adding and Subtracting Matrices
OBJ: 4-2.1 Adding and Subtracting Matrices STA: MS AII 7c | MS AII 7d
KEY: matrix addition | matrix
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