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 =8−558

Find the determinant det A of the matrix A shown.

A = [8 −5; 5 8]
det A =
2.Easy
A =−27−50

Find the determinant det A of the matrix A shown.

A = [−2 7; −5 0]
det A =
3.Medium
A =013510−42−4

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

A = [0 1 3; 5 1 0; −4 2 −4]
det A =
4.Medium
A =−1211B =1−3−31

Let C = AB for the matrices shown. Find the entry c11 (row 1, column 1).

A = [−1 2; 1 1]B = [1 −3; −3 1]
c11 =
5.Hard
A =5−5−31b =59

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

5x − 5y = 5−3x + y = 9
x =
6.Hard
A =−125−5b =012

Solve the system −x + 2y = 0 and 5x − 5y = 12. Find x.

−x + 2y = 05x − 5y = 12
x =

Answer key

  1. 1. det A = 89
  2. 2. det A = 35
  3. 3. det A = 62
  4. 4. c11 = −7
  5. 5. x = −5
  6. 6. x = 4.8

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