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 =6553

Find the determinant det A of the matrix A shown.

A = [6 5; 5 3]
det A =
2.Easy
A =−6−5−9−2

Find the determinant det A of the matrix A shown.

A = [−6 −5; −9 −2]
det A =
3.Medium
A =4−3−413−3−1−1−4

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

A = [4 −3 −4; 1 3 −3; −1 −1 −4]
det A =
4.Medium
A =−23−43B =−65−53

Let C = AB for the matrices shown. Find the entry c12 (row 1, column 2).

A = [−2 3; −4 3]B = [−6 5; −5 3]
c12 =
5.Hard
A =5−263b =1012

Solve the system 5x − 2y = 10 and 6x + 3y = 12. Find x.

5x − 2y = 106x + 3y = 12
x =
6.Hard
A =41−4−1

Find the larger eigenvalue λ of the matrix A shown.

A = [4 1; −4 −1]
λ =

Answer key

  1. 1. det A = −7
  2. 2. det A = −33
  3. 3. det A = −89
  4. 4. c12 = −1
  5. 5. x = 2
  6. 6. λ = 3

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