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 =−42−23

Find the determinant det A of the matrix A shown.

A = [−4 2; −2 3]
det A =
2.Easy
A =−62−3−8

Find the determinant det A of the matrix A shown.

A = [−6 2; −3 −8]
det A =
3.Medium
A =−6−35−4B =24−1−6

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

A = [−6 −3; 5 −4]B = [2 4; −1 −6]
c22 =
4.Medium
A =−2004−4−4−320

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

A = [−2 0 0; 4 −4 −4; −3 2 0]
det A =
5.Hard
A =−3−186

Find the larger eigenvalue λ of the matrix A shown.

A = [−3 −1; 8 6]
λ =
6.Hard
A =12−44b =111

Solve the system x + 2y = 1 and −4x + 4y = 11. Find x.

x + 2y = 1−4x + 4y = 11
x =

Answer key

  1. 1. det A = −8
  2. 2. det A = 54
  3. 3. c22 = 44
  4. 4. det A = −16
  5. 5. λ = 5
  6. 6. x = −1.5

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