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 =6−18−8

Find the determinant det A of the matrix A shown.

A = [6 −1; 8 −8]
det A =
2.Easy
A =−464−5

Find the determinant det A of the matrix A shown.

A = [−4 6; 4 −5]
det A =
3.Medium
A =2−505−3102−5

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

A = [2 −5 0; 5 −3 1; 0 2 −5]
det A =
4.Medium
A =−2−304B =10−25

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

A = [−2 −3; 0 4]B = [1 0; −2 5]
c22 =
5.Hard
A =5−26−2

Find the larger eigenvalue λ of the matrix A shown.

A = [5 −2; 6 −2]
λ =
6.Hard
A =−6−2−14b =82

Solve the system −6x − 2y = 8 and −x + 4y = 2. Find x.

−6x − 2y = 8−x + 4y = 2
x =

Answer key

  1. 1. det A = −40
  2. 2. det A = −4
  3. 3. det A = −99
  4. 4. c22 = 20
  5. 5. λ = 2
  6. 6. x = −1.385

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