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 =−575−9

Find the determinant det A of the matrix A shown.

A = [−5 7; 5 −9]
det A =
2.Easy
A =−9−967

Find the determinant det A of the matrix A shown.

A = [−9 −9; 6 7]
det A =
3.Medium
A =34−2124−41−5

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

A = [3 4 −2; 1 2 4; −4 1 −5]
det A =
4.Medium
A =35−31B =2326

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

A = [3 5; −3 1]B = [2 3; 2 6]
c21 =
5.Hard
A =1−2−24

Find the larger eigenvalue λ of the matrix A shown.

A = [1 −2; −2 4]
λ =
6.Hard
A =5−4−5−4b =109

Solve the system 5x − 4y = 10 and −5x − 4y = 9. Find x.

5x − 4y = 10−5x − 4y = 9
x =

Answer key

  1. 1. det A = 10
  2. 2. det A = −9
  3. 3. det A = −104
  4. 4. c21 = −4
  5. 5. λ = 5
  6. 6. x = 0.1

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