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 =6−2−74

Find the determinant det A of the matrix A shown.

A = [6 −2; −7 4]
det A =
2.Easy
A =−2−3−1−9

Find the determinant det A of the matrix A shown.

A = [−2 −3; −1 −9]
det A =
3.Medium
A =23−4105250

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

A = [2 3 −4; 1 0 5; 2 5 0]
det A =
4.Medium
A =1−642B =−5521

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

A = [1 −6; 4 2]B = [−5 5; 2 1]
c11 =
5.Hard
A =225−2b =−125

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

2x + 2y = −125x − 2y = 5
x =
6.Hard
A =−61−24b =−29

Solve the system −6x + y = −2 and −2x + 4y = 9. Find x.

−6x + y = −2−2x + 4y = 9
x =

Answer key

  1. 1. det A = 10
  2. 2. det A = 15
  3. 3. det A = −40
  4. 4. c11 = −17
  5. 5. x = −1
  6. 6. x = 0.7727

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