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 =4−3−30

Find the determinant det A of the matrix A shown.

A = [4 −3; −3 0]
det A =
2.Easy
A =−8−659

Find the determinant det A of the matrix A shown.

A = [−8 −6; 5 9]
det A =
3.Medium
A =1666B =2−5−43

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

A = [1 6; 6 6]B = [2 −5; −4 3]
c22 =
4.Medium
A =−20−1−13−42−51

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

A = [−2 0 −1; −1 3 −4; 2 −5 1]
det A =
5.Hard
A =6225b =−75

Solve the system 6x + 2y = −7 and 2x + 5y = 5. Find x.

6x + 2y = −72x + 5y = 5
x =
6.Hard
A =−6−642b =32

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

−6x − 6y = 34x + 2y = 2
x =

Answer key

  1. 1. det A = −9
  2. 2. det A = −42
  3. 3. c22 = −12
  4. 4. det A = 35
  5. 5. x = −1.731
  6. 6. x = 1.5

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