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 =40−1−7

Find the determinant det A of the matrix A shown.

A = [4 0; −1 −7]
det A =
2.Easy
A =−5−9−9−7

Find the determinant det A of the matrix A shown.

A = [−5 −9; −9 −7]
det A =
3.Medium
A =−4−1−24−241−1−2

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

A = [−4 −1 −2; 4 −2 4; 1 −1 −2]
det A =
4.Medium
A =1−56−6B =−65−5−1

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

A = [1 −5; 6 −6]B = [−6 5; −5 −1]
c22 =
5.Hard
A =2−145b =−6−8

Solve the system 2x − y = −6 and 4x + 5y = −8. Find x.

2x − y = −64x + 5y = −8
x =
6.Hard
A =623−1b =−5−3

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

6x + 2y = −53x − y = −3
x =

Answer key

  1. 1. det A = −28
  2. 2. det A = −46
  3. 3. det A = −40
  4. 4. c22 = 36
  5. 5. x = −2.714
  6. 6. x = −0.9167

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