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?

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

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

   • Yes: det(A) = 24
   • Yes: det(A) = -30
   • No: det(A) = 0
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
   • Yes: det(A) = 24
   • No: det(A) = 0
7. 7.

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

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

   Jun undoes the code table A = [3, 1; 5, 2] for a puzzle card. What is A⁻¹?

   • [2, 1; 5, 3]
   • [3, -1; -5, 2]
   • (1/11)[2, -1; -5, 3]
   • [2, -1; -5, 3]
9. 9.

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

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