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 =0530

Find the determinant det A of the matrix A shown.

A = [0 5; 3 0]
det A =
2.Easy
A =−31−83

Find the determinant det A of the matrix A shown.

A = [−3 1; −8 3]
det A =
3.Medium
A =5334B =−526−6

Let C = AB for the matrices shown. Find the entry c11 (row 1, column 1).

A = [5 3; 3 4]B = [−5 2; 6 −6]
c11 =
4.Medium
A =1−5−51−5−24−35

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

A = [1 −5 −5; 1 −5 −2; 4 −3 5]
det A =
5.Hard
A =−21−43

Find the larger eigenvalue λ of the matrix A shown.

A = [−2 1; −4 3]
λ =
6.Hard
A =−65−3−6b =10−6

Solve the system −6x + 5y = 10 and −3x − 6y = −6. Find x.

−6x + 5y = 10−3x − 6y = −6
x =

Answer key

  1. 1. det A = −15
  2. 2. det A = −1
  3. 3. c11 = −7
  4. 4. det A = −51
  5. 5. λ = 2
  6. 6. x = −0.5882

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