Determinants and inverses of 3 by 3 matrices

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Ari writes A = [2, 1, 3; 0, 4, 1; 1, 2, 5] in a notebook and expands along row 1. What is det(A)?

   25
2. 2.

   Bo writes A = [1, 2, 0; 3, 1, 2; 0, 1, 1] in a notebook and expands along row 1. What is det(A)?

   -7
3. 3.

   Jun needs the inverse of A = [1, 1, 0; 0, 1, 1; 0, 0, 1]. Which is it?

   • [−1, −1, 0; 0, −1, −1; 0, 0, −1]
   • [1, −1, 1; 0, 1, −1; 0, 0, 1]
   • [1, −1, 0; 0, 1, −1; 0, 0, 1]
4. 4.

   Kira needs the inverse of A = [1, 0, 0; 2, 1, 0; 0, 3, 1]. Which is it?

   • [1, 0, 0; −2, 1, 0; 0, −3, 1]
   • [1, 0, 0; −2, 1, 0; 6, −3, 1]
   • [1, 0, 0; 2, 1, 0; 0, 3, 1]
5. 5.

   Does Milo's A = [1, 2, 3; 4, 5, 6; 7, 8, 9] have an inverse?

   • No: det(A) = 0
   • Yes: det(A) = 45
   • Yes: no row is made of zeros
6. 6.

   Does Noah's A = [2, 0, 0; 0, 3, 0; 0, 0, 0] have an inverse?

   • Yes: det(A) = 6
   • Yes: det(A) = 5
   • No: det(A) = 0
7. 7.

   Pia's matrix has two equal rows. What is its determinant?

   • 0
   • 1
   • The row total
8. 8.

   What sign goes with the entry in row 2, column 1 when Ren expands?

   • ×
   • +
   • −
9. 9.

   Why does Tala expand along a row with zeros?

   • Zeros make det = 0
   • Zeros flip each sign
   • Zero entries drop their terms
10. 10.

    Zee swaps two rows of a matrix with det 7. What is the new determinant?

    • −7
    • 0
    • 7