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 =−5−69−3

Find the determinant det A of the matrix A shown.

A = [−5 −6; 9 −3]
det A =
2.Easy
A =−6−53−2

Find the determinant det A of the matrix A shown.

A = [−6 −5; 3 −2]
det A =
3.Medium
A =5−55−33140−4

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

A = [5 −5 5; −3 3 1; 4 0 −4]
det A =
4.Medium
A =420−1B =5−55−4

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

A = [4 2; 0 −1]B = [5 −5; 5 −4]
c22 =
5.Hard
A =4−1−7−2

Find the larger eigenvalue λ of the matrix A shown.

A = [4 −1; −7 −2]
λ =
6.Hard
A =−3−3−2−1b =−811

Solve the system −3x − 3y = −8 and −2x − y = 11. Find x.

−3x − 3y = −8−2x − y = 11
x =

Answer key

  1. 1. det A = 69
  2. 2. det A = 27
  3. 3. det A = −80
  4. 4. c22 = 4
  5. 5. λ = 5
  6. 6. x = −13.67

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