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 =−3−6−3−2

Find the determinant det A of the matrix A shown.

A = [−3 −6; −3 −2]
det A =
2.Easy
A =1−1−58

Find the determinant det A of the matrix A shown.

A = [1 −1; −5 8]
det A =
3.Medium
A =−254−522500

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

A = [−2 5 4; −5 2 2; 5 0 0]
det A =
4.Medium
A =5−1−6−2B =35−3−1

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

A = [5 −1; −6 −2]B = [3 5; −3 −1]
c21 =
5.Hard
A =−52−6−2b =9−8

Solve the system −5x + 2y = 9 and −6x − 2y = −8. Find x.

−5x + 2y = 9−6x − 2y = −8
x =
6.Hard
A =243−2

Find the larger eigenvalue λ of the matrix A shown.

A = [2 4; 3 −2]
λ =

Answer key

  1. 1. det A = −12
  2. 2. det A = 3
  3. 3. det A = 10
  4. 4. c21 = −12
  5. 5. x = −0.09091
  6. 6. λ = 4

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