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 =9989

Find the determinant det A of the matrix A shown.

A = [9 9; 8 9]
det A =
2.Easy
A =−68−6−7

Find the determinant det A of the matrix A shown.

A = [−6 8; −6 −7]
det A =
3.Medium
A =0−4−43−244−24

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

A = [0 −4 −4; 3 −2 4; 4 −2 4]
det A =
4.Medium
A =−603−4B =0−3−2−6

Let C = AB for the matrices shown. Find the entry c21 (row 2, column 1).

A = [−6 0; 3 −4]B = [0 −3; −2 −6]
c21 =
5.Hard
A =−16−44b =−4−3

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

−x + 6y = −4−4x + 4y = −3
x =
6.Hard
A =4−4−1−2b =−810

Solve the system 4x − 4y = −8 and −x − 2y = 10. Find x.

4x − 4y = −8−x − 2y = 10
x =

Answer key

  1. 1. det A = 9
  2. 2. det A = 90
  3. 3. det A = −24
  4. 4. c21 = 8
  5. 5. x = 0.1
  6. 6. x = −4.667

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