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 =−8701

Find the determinant det A of the matrix A shown.

A = [−8 7; 0 1]
det A =
2.Easy
A =1995

Find the determinant det A of the matrix A shown.

A = [1 9; 9 5]
det A =
3.Medium
A =5−432144−33

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

A = [5 −4 3; 2 1 4; 4 −3 3]
det A =
4.Medium
A =3−62−5B =−4−3−3−1

Let C = AB for the matrices shown. Find the entry c22 (row 2, column 2).

A = [3 −6; 2 −5]B = [−4 −3; −3 −1]
c22 =
5.Hard
A =−54−3−6b =8−4

Solve the system −5x + 4y = 8 and −3x − 6y = −4. Find x.

−5x + 4y = 8−3x − 6y = −4
x =
6.Hard
A =−2−1−80

Find the larger eigenvalue λ of the matrix A shown.

A = [−2 −1; −8 0]
λ =

Answer key

  1. 1. det A = −8
  2. 2. det A = −76
  3. 3. det A = 5
  4. 4. c22 = −1
  5. 5. x = −0.7619
  6. 6. λ = 2

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