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 =611−6

Find the determinant det A of the matrix A shown.

A = [6 1; 1 −6]
det A =
2.Easy
A =543−1

Find the determinant det A of the matrix A shown.

A = [5 4; 3 −1]
det A =
3.Medium
A =1−656B =5−2−11

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

A = [1 −6; 5 6]B = [5 −2; −1 1]
c22 =
4.Medium
A =66−52B =56−45

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

A = [6 6; −5 2]B = [5 6; −4 5]
c21 =
5.Hard
A =1111

Find the larger eigenvalue λ of the matrix A shown.

A = [1 1; 1 1]
λ =
6.Hard
A =551−5b =9−6

Solve the system 5x + 5y = 9 and x − 5y = −6. Find x.

5x + 5y = 9x − 5y = −6
x =

Answer key

  1. 1. det A = −37
  2. 2. det A = −17
  3. 3. c22 = −4
  4. 4. c21 = −33
  5. 5. λ = 2
  6. 6. x = 0.5

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