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 =−8601

Find the determinant det A of the matrix A shown.

A = [−8 6; 0 1]
det A =
2.Easy
A =39−6−7

Find the determinant det A of the matrix A shown.

A = [3 9; −6 −7]
det A =
3.Medium
A =−334543−533

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

A = [−3 3 4; 5 4 3; −5 3 3]
det A =
4.Medium
A =5302B =−450−2

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

A = [5 3; 0 2]B = [−4 5; 0 −2]
c22 =
5.Hard
A =−1−4−21b =120

Solve the system −x − 4y = 12 and −2x + y = 0. Find x.

−x − 4y = 12−2x + y = 0
x =
6.Hard
A =46−1−1

Find the larger eigenvalue λ of the matrix A shown.

A = [4 6; −1 −1]
λ =

Answer key

  1. 1. det A = −8
  2. 2. det A = 33
  3. 3. det A = 41
  4. 4. c22 = −4
  5. 5. x = −1.333
  6. 6. λ = 2

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