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 =5−3−3−8

Find the determinant det A of the matrix A shown.

A = [5 −3; −3 −8]
det A =
2.Easy
A =5−7−5−9

Find the determinant det A of the matrix A shown.

A = [5 −7; −5 −9]
det A =
3.Medium
A =−23−1−2B =1−313

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

A = [−2 3; −1 −2]B = [1 −3; 1 3]
c12 =
4.Medium
A =30−2505−5−24

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

A = [3 0 −2; 5 0 5; −5 −2 4]
det A =
5.Hard
A =−312−6b =−44

Solve the system −3x + y = −4 and 2x − 6y = 4. Find x.

−3x + y = −42x − 6y = 4
x =
6.Hard
A =−52−2−2b =−69

Solve the system −5x + 2y = −6 and −2x − 2y = 9. Find x.

−5x + 2y = −6−2x − 2y = 9
x =

Answer key

  1. 1. det A = −49
  2. 2. det A = −80
  3. 3. c12 = 15
  4. 4. det A = 50
  5. 5. x = 1.25
  6. 6. x = −0.4286

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