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 =5−805

Find the determinant det A of the matrix A shown.

A = [5 −8; 0 5]
det A =
2.Easy
A =−7794

Find the determinant det A of the matrix A shown.

A = [−7 7; 9 4]
det A =
3.Medium
A =−5263B =346−1

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

A = [−5 2; 6 3]B = [3 4; 6 −1]
c21 =
4.Medium
A =0−3−341−155−3

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

A = [0 −3 −3; 4 1 −1; 5 5 −3]
det A =
5.Hard
A =62−40

Find the larger eigenvalue λ of the matrix A shown.

A = [6 2; −4 0]
λ =
6.Hard
A =5−34−3b =−46

Solve the system 5x − 3y = −4 and 4x − 3y = 6. Find x.

5x − 3y = −44x − 3y = 6
x =

Answer key

  1. 1. det A = 25
  2. 2. det A = −91
  3. 3. c21 = 36
  4. 4. det A = −66
  5. 5. λ = 4
  6. 6. x = −10

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