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 =06−75

Find the determinant det A of the matrix A shown.

A = [0 6; −7 5]
det A =
2.Easy
A =−65−92

Find the determinant det A of the matrix A shown.

A = [−6 5; −9 2]
det A =
3.Medium
A =−25052−52−54

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

A = [−2 5 0; 5 2 −5; 2 −5 4]
det A =
4.Medium
A =−21−6−1B =−32−4−5

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

A = [−2 1; −6 −1]B = [−3 2; −4 −5]
c21 =
5.Hard
A =3−2−14

Find the larger eigenvalue λ of the matrix A shown.

A = [3 −2; −1 4]
λ =
6.Hard
A =515−5b =5−2

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

5x + y = 55x − 5y = −2
x =

Answer key

  1. 1. det A = 42
  2. 2. det A = 33
  3. 3. det A = −116
  4. 4. c21 = 22
  5. 5. λ = 5
  6. 6. x = 0.7667

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