Determinants and inverse matrices

Answer Key - Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. Read this first

   Number table A, 2 by 2

   Row 1 is 5, 2; row 2 is 4, 3. The down diagonal (5 to 3) is blue; the up diagonal (4 to 2) is orange.

2. 1.

   Esme writes matrix A = [5, 2; 4, 3] in a notebook. The down diagonal gives 5 × 3 and the up diagonal gives 2 × 4. What is det(A)?

   7

3. Number table A, 2 by 2

   Row 1 is 6, 1; row 2 is 3, 4. The down diagonal (6 to 4) is blue; the up diagonal (3 to 1) is orange.

4. 2.

   Jun copies matrix A = [6, 1; 3, 4] from the board. The down diagonal gives 6 × 4 and the up diagonal gives 1 × 3. What is det(A)?

   21
5. 3.

   Luz checks matrix A = [8, 3; 5, 2] on a worksheet. What is det(A)?

   1
6. 4.

   Noah finds matrix A = [9, 4; 5, 3] in a math book. What is det(A)?

   7

7. A⁻¹ = (1/det(A)) × [d, -b; -c, a]

   Swap the down diagonal, change the signs of the up diagonal, then divide every entry by det(A).

8. 5.

   Pia finds the inverse of A = [5, 2; 3, 4], and det(A) = 14. What is the top-right entry of A⁻¹?

   -1/7
9. 6.

   Ren finds the inverse of A = [7, 2; 3, 4], and det(A) = 22. What is the bottom-left entry of A⁻¹?

   -3/22
10. 7.

    Tala finds the inverse of A = [5, 3; 4, 6], and det(A) = 18. What is the top-left entry of A⁻¹?

    1/3
11. 8.

    Esme finds the inverse of A = [6, 4; 1, 3], and det(A) = 14. What is the bottom-right entry of A⁻¹?

    3/7
12. 9.

    Kira checks the table A = [2, 5; 4, 10] before finding its inverse. Does A have an inverse?

    • Yes: det(A) = -30
    • No: det(A) = 0
    • Yes: det(A) = 0
    • Yes: det(A) = 40
13. 10.

    Luz checks the table A = [2, 3; 6, 1] before finding its inverse. Does A have an inverse?

    • No: det(A) = 0
    • Yes: det(A) = -16
    • Yes: det(A) = 20