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 =9−661

Find the determinant det A of the matrix A shown.

A = [9 −6; 6 1]
det A =
2.Easy
A =9−9−42

Find the determinant det A of the matrix A shown.

A = [9 −9; −4 2]
det A =
3.Medium
A =04−5−5B =3−1−45

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

A = [0 4; −5 −5]B = [3 −1; −4 5]
c11 =
4.Medium
A =4−1510−5−51−2

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

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

Solve the system −5x − y = −1 and −4x − 2y = −1. Find x.

−5x − y = −1−4x − 2y = −1
x =
6.Hard
A =26−65b =−11−8

Solve the system 2x + 6y = −11 and −6x + 5y = −8. Find x.

2x + 6y = −11−6x + 5y = −8
x =

Answer key

  1. 1. det A = 45
  2. 2. det A = −18
  3. 3. c11 = −16
  4. 4. det A = −2
  5. 5. x = 0.1667
  6. 6. x = −0.1522

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