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 =221−4

Find the determinant det A of the matrix A shown.

A = [2 2; 1 −4]
det A =
2.Easy
A =−89−1−5

Find the determinant det A of the matrix A shown.

A = [−8 9; −1 −5]
det A =
3.Medium
A =−121−54−2135

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

A = [−1 2 1; −5 4 −2; 1 3 5]
det A =
4.Medium
A =−4231B =−5222

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

A = [−4 2; 3 1]B = [−5 2; 2 2]
c12 =
5.Hard
A =−33−53b =−9−7

Solve the system −3x + 3y = −9 and −5x + 3y = −7. Find x.

−3x + 3y = −9−5x + 3y = −7
x =
6.Hard
A =−5−512b =−910

Solve the system −5x − 5y = −9 and x + 2y = 10. Find x.

−5x − 5y = −9x + 2y = 10
x =

Answer key

  1. 1. det A = −10
  2. 2. det A = 49
  3. 3. det A = 1
  4. 4. c12 = −4
  5. 5. x = −1
  6. 6. x = −6.4

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