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 =−430−6

Find the determinant det A of the matrix A shown.

A = [−4 3; 0 −6]
det A =
2.Easy
A =40−9−2

Find the determinant det A of the matrix A shown.

A = [4 0; −9 −2]
det A =
3.Medium
A =05−55−15403

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

A = [0 5 −5; 5 −1 5; 4 0 3]
det A =
4.Medium
A =−16−34B =−40−62

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

A = [−1 6; −3 4]B = [−4 0; −6 2]
c21 =
5.Hard
A =54−5−6b =−1111

Solve the system 5x + 4y = −11 and −5x − 6y = 11. Find x.

5x + 4y = −11−5x − 6y = 11
x =
6.Hard
A =23−2−6b =−20

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

2x + 3y = −2−2x − 6y = 0
x =

Answer key

  1. 1. det A = 24
  2. 2. det A = −8
  3. 3. det A = 5
  4. 4. c21 = −12
  5. 5. x = −2.2
  6. 6. x = −2

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