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 =−7−6−6−4

Find the determinant det A of the matrix A shown.

A = [−7 −6; −6 −4]
det A =
2.Easy
A =−6−98−8

Find the determinant det A of the matrix A shown.

A = [−6 −9; 8 −8]
det A =
3.Medium
A =−5−2−2−4B =1−5−6−6

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

A = [−5 −2; −2 −4]B = [1 −5; −6 −6]
c12 =
4.Medium
A =−3−4−1−3−3405−2

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

A = [−3 −4 −1; −3 −3 4; 0 5 −2]
det A =
5.Hard
A =2−531b =−98

Solve the system 2x − 5y = −9 and 3x + y = 8. Find x.

2x − 5y = −93x + y = 8
x =
6.Hard
A =64−3−6b =−42

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

6x + 4y = −4−3x − 6y = 2
x =

Answer key

  1. 1. det A = −8
  2. 2. det A = 120
  3. 3. c12 = 37
  4. 4. det A = 81
  5. 5. x = 1.824
  6. 6. x = −0.6667

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