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 =−5−5−85

Find the determinant det A of the matrix A shown.

A = [−5 −5; −8 5]
det A =
2.Easy
A =22−67

Find the determinant det A of the matrix A shown.

A = [2 2; −6 7]
det A =
3.Medium
A =−121−504−1−54

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

A = [−1 2 1; −5 0 4; −1 −5 4]
det A =
4.Medium
A =−2033B =−1−52−4

Let C = AB for the matrices shown. Find the entry c22 (row 2, column 2).

A = [−2 0; 3 3]B = [−1 −5; 2 −4]
c22 =
5.Hard
A =−2273

Find the larger eigenvalue λ of the matrix A shown.

A = [−2 2; 7 3]
λ =
6.Hard
A =−6−315b =124

Solve the system −6x − 3y = 12 and x + 5y = 4. Find x.

−6x − 3y = 12x + 5y = 4
x =

Answer key

  1. 1. det A = −65
  2. 2. det A = 26
  3. 3. det A = 37
  4. 4. c22 = −27
  5. 5. λ = 5
  6. 6. x = −2.667

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