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 =−6−162

Find the determinant det A of the matrix A shown.

A = [−6 −1; 6 2]
det A =
2.Easy
A =−5073

Find the determinant det A of the matrix A shown.

A = [−5 0; 7 3]
det A =
3.Medium
A =−12−33B =−4−6−4−4

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

A = [−1 2; −3 3]B = [−4 −6; −4 −4]
c11 =
4.Medium
A =4456B =−653−6

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

A = [4 4; 5 6]B = [−6 5; 3 −6]
c22 =
5.Hard
A =56−4−5

Find the larger eigenvalue λ of the matrix A shown.

A = [5 6; −4 −5]
λ =
6.Hard
A =5−1−44b =12−10

Solve the system 5x − y = 12 and −4x + 4y = −10. Find x.

5x − y = 12−4x + 4y = −10
x =

Answer key

  1. 1. det A = −6
  2. 2. det A = −15
  3. 3. c11 = −4
  4. 4. c22 = −11
  5. 5. λ = 1
  6. 6. x = 2.375

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