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 =−4−296

Find the determinant det A of the matrix A shown.

A = [−4 −2; 9 6]
det A =
2.Easy
A =7−8−3−6

Find the determinant det A of the matrix A shown.

A = [7 −8; −3 −6]
det A =
3.Medium
A =4−122521−11

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

A = [4 −1 2; 2 5 2; 1 −1 1]
det A =
4.Medium
A =50−23B =1−2−24

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

A = [5 0; −2 3]B = [1 −2; −2 4]
c21 =
5.Hard
A =11−4−1b =99

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

x + y = 9−4x − y = 9
x =
6.Hard
A =−1−44−5b =312

Solve the system −x − 4y = 3 and 4x − 5y = 12. Find x.

−x − 4y = 34x − 5y = 12
x =

Answer key

  1. 1. det A = −6
  2. 2. det A = −66
  3. 3. det A = 14
  4. 4. c21 = −8
  5. 5. x = −6
  6. 6. x = 1.571

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