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 =1−820

Find the determinant det A of the matrix A shown.

A = [1 −8; 2 0]
det A =
2.Easy
A =−6978

Find the determinant det A of the matrix A shown.

A = [−6 9; 7 8]
det A =
3.Medium
A =−1−55−5−123−11

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

A = [−1 −5 5; −5 −1 2; 3 −1 1]
det A =
4.Medium
A =232−6B =00−12

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

A = [2 3; 2 −6]B = [0 0; −1 2]
c21 =
5.Hard
A =53−5−3

Find the larger eigenvalue λ of the matrix A shown.

A = [5 3; −5 −3]
λ =
6.Hard
A =−3226b =912

Solve the system −3x + 2y = 9 and 2x + 6y = 12. Find x.

−3x + 2y = 92x + 6y = 12
x =

Answer key

  1. 1. det A = 16
  2. 2. det A = −111
  3. 3. det A = −16
  4. 4. c21 = 6
  5. 5. λ = 2
  6. 6. x = −1.364

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