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 =−64−6−8

Find the determinant det A of the matrix A shown.

A = [−6 4; −6 −8]
det A =
2.Easy
A =6−9−7−1

Find the determinant det A of the matrix A shown.

A = [6 −9; −7 −1]
det A =
3.Medium
A =44−4−3124−1−3

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

A = [4 4 −4; −3 1 2; 4 −1 −3]
det A =
4.Medium
A =−3−2−4−1B =−21−2−1

Let C = AB for the matrices shown. Find the entry c12 (row 1, column 2).

A = [−3 −2; −4 −1]B = [−2 1; −2 −1]
c12 =
5.Hard
A =11−8−5

Find the larger eigenvalue λ of the matrix A shown.

A = [1 1; −8 −5]
λ =
6.Hard
A =−1662b =−49

Solve the system −x + 6y = −4 and 6x + 2y = 9. Find x.

−x + 6y = −46x + 2y = 9
x =

Answer key

  1. 1. det A = 72
  2. 2. det A = −69
  3. 3. det A = −4
  4. 4. c12 = −1
  5. 5. λ = −1
  6. 6. x = 1.632

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