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 7, 3; row 2 is 2, 5. The down diagonal (7 to 5) is blue; the up diagonal (2 to 3) is orange.

2. 1.

   Kira reads matrix A = [7, 3; 2, 5] in a math book. The down diagonal gives 7 × 5 and the up diagonal gives 3 × 2. What is det(A)?

   29
3. 2.

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

   1
4. 3.

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

   7

5. 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).

6. 4.

   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
7. 5.

   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
8. 6.

   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
9. 7.

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

   4/3
10. 8.

    Jun wants to decode messages coded with the table A = [6, 4; 9, 6]. Does A have an inverse?

    • Yes: det(A) = 0
    • No: det(A) = 0
    • Yes: det(A) = -30
    • Yes: det(A) = 72
11. 9.

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

    • Yes: det(A) = 40
    • Yes: det(A) = 0
    • No: det(A) = 0
    • Yes: det(A) = -30
12. 10.

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

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