Determinants and inverse matrices

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Noah unscrambles a message coded with A = [3, -2; 4, 1]. What is A⁻¹?

   • (1/5)[-1, -2; 4, -3]
   • (1/11)[1, -2; 4, 3]
   • [1, 2; -4, 3]
   • (1/11)[1, 2; -4, 3]
   • (1/11)[3, 2; -4, 1]
2. 2.

   Pia checks the table A = [-2, 6; 1, -3] for a puzzle card. What is A⁻¹?

   • [-3, 6; 1, -2]
   • No inverse: det(A) = 0
   • [-3, -6; -1, -2]
   • (1/12)[-3, -6; -1, -2]
3. 3.

   Ren works out the inverse of A = [2, 5; 1, -2] on a worksheet. What is A⁻¹?

   • (1/9)[2, 5; 1, -2]
   • [-2, -5; -1, 2]
   • (1/9)[-2, 5; 1, 2]
   • (1/9)[2, -5; -1, -2]
4. 4.

   Tala checks the table A = [6, -4; -3, 2] for a puzzle card. What is A⁻¹?

   • No inverse: det(A) = 0
   • (1/24)[2, 4; 3, 6]
   • [2, -4; -3, 6]
   • [2, 4; 3, 6], ignoring the determinant
5. 5.

   Zee wants the table A = [k, 7; 3, 5] to have no inverse. What value of k makes that happen?

   21/5
6. 6.

   Bo wants the table A = [5, k; 3, 6] to have no inverse. What value of k makes that happen?

   10
7. 7.

   Esme wants the table A = [2, 9; 4, k] to have no inverse. What value of k makes that happen?

   18
8. 8.

   Jun wants the table A = [9, 6; k, 2] to have no inverse. What value of k makes that happen?

   3
9. 9.

   Luz reshapes a 2-by-2 rug square with M = [4, 1; 2, -1]. What is the area of the image, in square units?

   24
10. 10.

    Pia reshapes a 4-by-1 rug strip with M = [1, 3; 2, 1]. What is the area of the image, in square units?

    20