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 =−3−1−20

Find the determinant det A of the matrix A shown.

A = [−3 −1; −2 0]
det A =
2.Easy
A =59−8−3

Find the determinant det A of the matrix A shown.

A = [5 9; −8 −3]
det A =
3.Medium
A =−25−453−54−52

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

A = [−2 5 −4; 5 3 −5; 4 −5 2]
det A =
4.Medium
A =4−14−1B =−351−1

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

A = [4 −1; 4 −1]B = [−3 5; 1 −1]
c11 =
5.Hard
A =533−3

Find the larger eigenvalue λ of the matrix A shown.

A = [5 3; 3 −3]
λ =
6.Hard
A =−4−3−5−2b =−8−2

Solve the system −4x − 3y = −8 and −5x − 2y = −2. Find x.

−4x − 3y = −8−5x − 2y = −2
x =

Answer key

  1. 1. det A = −2
  2. 2. det A = 57
  3. 3. det A = 36
  4. 4. c11 = −13
  5. 5. λ = 6
  6. 6. x = −1.429

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