Matrices & determinants worksheet with answers

Free printable Matrices & determinants worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
A =−5−1−59

Find the determinant det A of the matrix A shown.

A = [−5 −1; −5 9]
det A =
2.Easy
A =5−18−7

Find the determinant det A of the matrix A shown.

A = [5 −1; 8 −7]
det A =
3.Medium
A =−3−542−1−5055

Find the determinant det A of the 3×3 matrix A shown.

A = [−3 −5 4; 2 −1 −5; 0 5 5]
det A =
4.Medium
A =6−5−31B =622−5

Let C = AB for the matrices shown. Find the entry c12 (row 1, column 2).

A = [6 −5; −3 1]B = [6 2; 2 −5]
c12 =
5.Hard
A =−2−555b =62

Solve the system −2x − 5y = 6 and 5x + 5y = 2. Find x.

−2x − 5y = 65x + 5y = 2
x =
6.Hard
A =−226−1b =−9−9

Solve the system −2x + 2y = −9 and 6x − y = −9. Find x.

−2x + 2y = −96x − y = −9
x =

Answer key

  1. 1. det A = −50
  2. 2. det A = −27
  3. 3. det A = 30
  4. 4. c12 = 37
  5. 5. x = 2.667
  6. 6. x = −2.7

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