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 =−3−9−9−8

Find the determinant det A of the matrix A shown.

A = [−3 −9; −9 −8]
det A =
2.Easy
A =10−23

Find the determinant det A of the matrix A shown.

A = [1 0; −2 3]
det A =
3.Medium
A =2254−2−3−15−4

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

A = [2 2 5; 4 −2 −3; −1 5 −4]
det A =
4.Medium
A =−5300B =5−52−1

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

A = [−5 3; 0 0]B = [5 −5; 2 −1]
c11 =
5.Hard
A =6−61−3b =−6−4

Solve the system 6x − 6y = −6 and x − 3y = −4. Find x.

6x − 6y = −6x − 3y = −4
x =
6.Hard
A =−2−4−20

Find the larger eigenvalue λ of the matrix A shown.

A = [−2 −4; −2 0]
λ =

Answer key

  1. 1. det A = −57
  2. 2. det A = 3
  3. 3. det A = 174
  4. 4. c11 = −19
  5. 5. x = 0.5
  6. 6. λ = 2

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