Determinants and inverses of 3 by 3 matrices

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Ari's 3 by 3 matrices have det(A) = 3 and det(B) = 4. A code is made by multiplying them. What is det(AB)?

   12
2. 2.

   Bo's 3 by 3 matrices have det(A) = -2 and det(B) = 7. A code is made by multiplying them. What is det(AB)?

   -14
3. 3.

   Jun solves Ax = (6, 3, 2) with A⁻¹ = [1, −1, 1; 0, 1, −1; 0, 0, 1]. What is x?

   • (11, 5, 2)
   • (5, 1, 2)
   • (6, 3, 2)
4. 4.

   Kira's 3 by 3 matrix A has det(A) = 5. What is det(2A)?

   • 10
   • 20
   • 40
5. 5.

   Milo says the row-1 expansion of a 3 by 3 determinant adds all three terms. Agree or disagree?

   • Agree: the three terms are added
   • Agree: signs matter just for 2 by 2
   • Disagree: the middle is subtracted
6. 6.

   Noah gets 23 for det [2, 1, 3; 0, 4, 1; 1, 2, 5] by adding all three terms. Agree or disagree?

   • Agree: adding the terms is right
   • Agree: 23 is the sum of entries
   • Disagree: it is 25
7. 7.

   Pia says a matrix with a zero entry can't have an inverse. Agree or disagree?

   • Agree: a zero breaks the inverse
   • Agree: zeros make det 0
   • Disagree: only det = 0 rules it out
8. 8.

   Which of Ren's matrices has no inverse?

   • [1, 2, 3; 0, 4, 6; 0, 0, 1]
   • [1, 2, 3; 2, 4, 6; 0, 1, 1]
   • [1, 0, 0; 0, 2, 0; 0, 0, 3]
9. 9.

   Which of Tala's matrices has determinant 1?

   • [2, 4, 2; 0, 1, 3; 0, 0, 1]
   • [1, 4, 2; 0, 1, 3; 0, 0, 1]
   • [1, 4, 2; 0, 0, 3; 0, 0, 1]
10. 10.

    Zee's matrix has det 3. How does it change the volume of a cube it transforms?

    • It cubes the volume
    • It adds 3 to the volume
    • It triples the volume