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 =588−9

Find the determinant det A of the matrix A shown.

A = [5 8; 8 −9]
det A =
2.Easy
A =−35−37

Find the determinant det A of the matrix A shown.

A = [−3 5; −3 7]
det A =
3.Medium
A =−1−2−202−1−4−20

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

A = [−1 −2 −2; 0 2 −1; −4 −2 0]
det A =
4.Medium
A =0−302B =−6656

Let C = AB for the matrices shown. Find the entry c22 (row 2, column 2).

A = [0 −3; 0 2]B = [−6 6; 5 6]
c22 =
5.Hard
A =5−2−46b =0−3

Solve the system 5x − 2y = 0 and −4x + 6y = −3. Find x.

5x − 2y = 0−4x + 6y = −3
x =
6.Hard
A =−4−414b =−96

Solve the system −4x − 4y = −9 and x + 4y = 6. Find x.

−4x − 4y = −9x + 4y = 6
x =

Answer key

  1. 1. det A = −109
  2. 2. det A = −6
  3. 3. det A = −22
  4. 4. c22 = 12
  5. 5. x = −0.2727
  6. 6. x = 1

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