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 =6−4−57

Find the determinant det A of the matrix A shown.

A = [6 −4; −5 7]
det A =
2.Easy
A =−8731

Find the determinant det A of the matrix A shown.

A = [−8 7; 3 1]
det A =
3.Medium
A =−6−426B =−5−4−25

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

A = [−6 −4; 2 6]B = [−5 −4; −2 5]
c21 =
4.Medium
A =5−2−1−1302−25

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

A = [5 −2 −1; −1 3 0; 2 −2 5]
det A =
5.Hard
A =0−257

Find the larger eigenvalue λ of the matrix A shown.

A = [0 −2; 5 7]
λ =
6.Hard
A =2−53−2b =−44

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

2x − 5y = −43x − 2y = 4
x =

Answer key

  1. 1. det A = 22
  2. 2. det A = −29
  3. 3. c21 = −22
  4. 4. det A = 69
  5. 5. λ = 5
  6. 6. x = 2.545

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