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 =−98−30

Find the determinant det A of the matrix A shown.

A = [−9 8; −3 0]
det A =
2.Easy
A =22−6−2

Find the determinant det A of the matrix A shown.

A = [2 2; −6 −2]
det A =
3.Medium
A =3−4153−5141

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

A = [3 −4 1; 5 3 −5; 1 4 1]
det A =
4.Medium
A =−360−5B =0316

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

A = [−3 6; 0 −5]B = [0 3; 1 6]
c21 =
5.Hard
A =4−217

Find the larger eigenvalue λ of the matrix A shown.

A = [4 −2; 1 7]
λ =
6.Hard
A =−23−3−4b =−25

Solve the system −2x + 3y = −2 and −3x − 4y = 5. Find x.

−2x + 3y = −2−3x − 4y = 5
x =

Answer key

  1. 1. det A = 24
  2. 2. det A = 8
  3. 3. det A = 126
  4. 4. c21 = −5
  5. 5. λ = 6
  6. 6. x = −0.4118

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