Determinants and inverses of 3 by 3 matrices

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   Ari's robot stores A = [2, 5, 1; 0, 3, 4; 0, 0, 4], with zeros below the diagonal. What is det(A)?

   24
2. 2.

   Bo's robot stores A = [1, 5, 1; 0, 5, 4; 0, 0, 2], with zeros below the diagonal. What is det(A)?

   10
3. 3.

   Esme's robot stores A = [3, 5, 1; 0, 2, 4; 0, 0, 3], with zeros below the diagonal. What is det(A)?

   18

4. Read this first

   Number table for A = [2, 1, 3; 0, 4, 1; 1, 2, 5] (sign pattern for row 1: +, −, +)

   row	column 1	column 2	column 3
   1	2	1	3
   2	0	4	1
   3	1	2	5

5. 4.

   Using the table, which numbers make the minor for the 2 in row 1, Jun?

   • 4, 1, 2, 5
   • 0, 4, 1, 2
   • 1, 3, 2, 5
6. 5.

   Using the table, what signs does Kira put on the three terms of row 1?

   • +, +, +
   • +, −, +
   • −, +, −
7. 6.

   Using the table, what is the minor for the 1 in row 1, Luz?

   • 18
   • 1
   • −1
8. 7.

   Milo's 3 by 3 matrix has determinant 6. What does that tell Milo?

   • It is the identity
   • It has no inverse
   • It has an inverse
9. 8.

   What does the 3 by 3 identity matrix I look like on Pia's sheet?

   • 0s on the diagonal, 1s elsewhere
   • 1s on the diagonal, 0s elsewhere
   • 1 in each of its nine cells
10. 9.

    How can Ren check that B is the inverse of A?

    • Add: A + B should be 0
    • Check det(B) = det(A)
    • Multiply: A × B should be I
11. 10.

    Zee multiplies a matrix A by the identity I. What comes out?

    • The identity I
    • Matrix A, unchanged
    • A matrix of zeros