Determinants and inverse matrices

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Milo writes matrix A = [-3, 4; 2, 5] on a worksheet. What is det(A)?

   -23
2. 2.

   Noah copies matrix A = [7, 2; 3, -4] from the board. What is det(A)?

   -34
3. 3.

   Pia reads matrix A = [-6, 5; 2, 3] in a math book. What is det(A)?

   -28
4. 4.

   Tala wants to decode messages coded with the table A = [-2, 6; 3, -9]. Does A have an inverse?

   • Yes: det(A) = 15
   • Yes: det(A) = 0
   • Yes: det(A) = 36
   • No: det(A) = 0
5. 5.

   Zee checks the table A = [2, -3; 4, 6] before finding its inverse. Does A have an inverse?

   • No: det(A) = 0
   • Yes: det(A) = -30
   • Yes: det(A) = 24
6. 6.

   Bo checks the table A = [4, -6; -2, 3] before finding its inverse. Does A have an inverse?

   • Yes: det(A) = -18
   • Yes: det(A) = 0
   • No: det(A) = 0
   • Yes: det(A) = 24
7. 7.

   Esme wants to decode messages coded with the table A = [5, 2; -10, 4]. Does A have an inverse?

   • Yes: det(A) = 40
   • No: det(A) = 0
   • Yes: det(A) = 50
8. 8.

   Kira undoes the code table A = [4, 3; 2, 1] for a puzzle card. What is A⁻¹?

   • (1/2)[-4, 3; 2, -1]
   • (1/2)[-1, 3; 2, -4]
   • [1, -3; -2, 4]
   • (1/2)[-1, -3; -2, -4]
   • (1/10)[1, -3; -2, 4]
9. 9.

   Luz unscrambles a message coded with A = [5, 2; 7, 3]. What is A⁻¹?

   • (1/29)[3, -2; -7, 5]
   • [3, 2; 7, 5]
   • [5, -2; -7, 3]
   • [3, -2; -7, 5]
10. 10.

    Milo works out the inverse of A = [3, 2; 1, 3] on a worksheet. What is A⁻¹?

    • (1/11)[3, -2; -1, 3]
    • (1/7)[3, 2; 1, 3]
    • (1/7)[3, -2; -1, 3]
    • [3, -2; -1, 3]