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 =−29−2−9

Find the determinant det A of the matrix A shown.

A = [−2 9; −2 −9]
det A =
2.Easy
A =0−9−1−8

Find the determinant det A of the matrix A shown.

A = [0 −9; −1 −8]
det A =
3.Medium
A =−3−4−4−53−101−3

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

A = [−3 −4 −4; −5 3 −1; 0 1 −3]
det A =
4.Medium
A =5−5−11B =64−20

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

A = [5 −5; −1 1]B = [6 4; −2 0]
c21 =
5.Hard
A =−56−62b =−812

Solve the system −5x + 6y = −8 and −6x + 2y = 12. Find x.

−5x + 6y = −8−6x + 2y = 12
x =
6.Hard
A =−36−811

Find the larger eigenvalue λ of the matrix A shown.

A = [−3 6; −8 11]
λ =

Answer key

  1. 1. det A = 36
  2. 2. det A = −9
  3. 3. det A = 104
  4. 4. c21 = −8
  5. 5. x = −3.385
  6. 6. λ = 5

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