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 =−1−661

Find the determinant det A of the matrix A shown.

A = [−1 −6; 6 1]
det A =
2.Easy
A =5−649

Find the determinant det A of the matrix A shown.

A = [5 −6; 4 9]
det A =
3.Medium
A =−1−30−1−5−54−50

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

A = [−1 −3 0; −1 −5 −5; 4 −5 0]
det A =
4.Medium
A =−5−333B =−132−5

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

A = [−5 −3; 3 3]B = [−1 3; 2 −5]
c21 =
5.Hard
A =5−42−4

Find the larger eigenvalue λ of the matrix A shown.

A = [5 −4; 2 −4]
λ =
6.Hard
A =−36−52b =−12−5

Solve the system −3x + 6y = −12 and −5x + 2y = −5. Find x.

−3x + 6y = −12−5x + 2y = −5
x =

Answer key

  1. 1. det A = 35
  2. 2. det A = 69
  3. 3. det A = 85
  4. 4. c21 = 3
  5. 5. λ = 4
  6. 6. x = 0.25

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