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 =70−3−7

Find the determinant det A of the matrix A shown.

A = [7 0; −3 −7]
det A =
2.Easy
A =−4540

Find the determinant det A of the matrix A shown.

A = [−4 5; 4 0]
det A =
3.Medium
A =30−3−3B =5163

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

A = [3 0; −3 −3]B = [5 1; 6 3]
c12 =
4.Medium
A =−5−2−2−525−5−52

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

A = [−5 −2 −2; −5 2 5; −5 −5 2]
det A =
5.Hard
A =1−1−11

Find the larger eigenvalue λ of the matrix A shown.

A = [1 −1; −1 1]
λ =
6.Hard
A =6−61−6b =−79

Solve the system 6x − 6y = −7 and x − 6y = 9. Find x.

6x − 6y = −7x − 6y = 9
x =

Answer key

  1. 1. det A = −49
  2. 2. det A = −20
  3. 3. c12 = 3
  4. 4. det A = −185
  5. 5. λ = 2
  6. 6. x = −3.2

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