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 =−99−87

Find the determinant det A of the matrix A shown.

A = [−9 9; −8 7]
det A =
2.Easy
A =0−86−9

Find the determinant det A of the matrix A shown.

A = [0 −8; 6 −9]
det A =
3.Medium
A =−2−31−1B =−6−403

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

A = [−2 −3; 1 −1]B = [−6 −4; 0 3]
c21 =
4.Medium
A =3−642B =5−4−64

Let C = AB for the matrices shown. Find the entry c12 (row 1, column 2).

A = [3 −6; 4 2]B = [5 −4; −6 4]
c12 =
5.Hard
A =6−1−6−1b =−6−11

Solve the system 6x − y = −6 and −6x − y = −11. Find x.

6x − y = −6−6x − y = −11
x =
6.Hard
A =−1−3−51

Find the larger eigenvalue λ of the matrix A shown.

A = [−1 −3; −5 1]
λ =

Answer key

  1. 1. det A = 9
  2. 2. det A = 48
  3. 3. c21 = −6
  4. 4. c12 = −36
  5. 5. x = 0.4167
  6. 6. λ = 4

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