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 =−98−99

Find the determinant det A of the matrix A shown.

A = [−9 8; −9 9]
det A =
2.Easy
A =88−3−5

Find the determinant det A of the matrix A shown.

A = [8 8; −3 −5]
det A =
3.Medium
A =00−3−2B =0−5−35

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

A = [0 0; −3 −2]B = [0 −5; −3 5]
c22 =
4.Medium
A =−5−4−64B =−43−26

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

A = [−5 −4; −6 4]B = [−4 3; −2 6]
c21 =
5.Hard
A =54−8−7

Find the larger eigenvalue λ of the matrix A shown.

A = [5 4; −8 −7]
λ =
6.Hard
A =23−3−4b =84

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

2x + 3y = 8−3x − 4y = 4
x =

Answer key

  1. 1. det A = −9
  2. 2. det A = −16
  3. 3. c22 = 5
  4. 4. c21 = 16
  5. 5. λ = 1
  6. 6. x = −44

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