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 =−9−32−1

Find the determinant det A of the matrix A shown.

A = [−9 −3; 2 −1]
det A =
2.Easy
A =−6323

Find the determinant det A of the matrix A shown.

A = [−6 3; 2 3]
det A =
3.Medium
A =325−2441−3−1

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

A = [3 2 5; −2 4 4; 1 −3 −1]
det A =
4.Medium
A =322−5B =−661−1

Let C = AB for the matrices shown. Find the entry c11 (row 1, column 1).

A = [3 2; 2 −5]B = [−6 6; 1 −1]
c11 =
5.Hard
A =6−39−6

Find the larger eigenvalue λ of the matrix A shown.

A = [6 −3; 9 −6]
λ =
6.Hard
A =−1−3−6−2b =7−3

Solve the system −x − 3y = 7 and −6x − 2y = −3. Find x.

−x − 3y = 7−6x − 2y = −3
x =

Answer key

  1. 1. det A = 15
  2. 2. det A = −24
  3. 3. det A = 38
  4. 4. c11 = −16
  5. 5. λ = 3
  6. 6. x = 1.438

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