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 =0−925

Find the determinant det A of the matrix A shown.

A = [0 −9; 2 5]
det A =
2.Easy
A =−65−2−6

Find the determinant det A of the matrix A shown.

A = [−6 5; −2 −6]
det A =
3.Medium
A =1−1−40224−20

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

A = [1 −1 −4; 0 2 2; 4 −2 0]
det A =
4.Medium
A =30−11B =−3−513

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

A = [3 0; −1 1]B = [−3 −5; 1 3]
c21 =
5.Hard
A =4242

Find the larger eigenvalue λ of the matrix A shown.

A = [4 2; 4 2]
λ =
6.Hard
A =−54−24b =111

Solve the system −5x + 4y = 1 and −2x + 4y = 11. Find x.

−5x + 4y = 1−2x + 4y = 11
x =

Answer key

  1. 1. det A = 18
  2. 2. det A = 46
  3. 3. det A = 28
  4. 4. c21 = 4
  5. 5. λ = 6
  6. 6. x = 3.333

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