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 =−94−1−2

Find the determinant det A of the matrix A shown.

A = [−9 4; −1 −2]
det A =
2.Easy
A =45−30

Find the determinant det A of the matrix A shown.

A = [4 5; −3 0]
det A =
3.Medium
A =−3445−21−3−4−5

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

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

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

A = [−1 −2; −4 −3]B = [4 −4; −1 −1]
c21 =
5.Hard
A =−14−58

Find the larger eigenvalue λ of the matrix A shown.

A = [−1 4; −5 8]
λ =
6.Hard
A =−2−6−62b =26

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

−2x − 6y = 2−6x + 2y = 6
x =

Answer key

  1. 1. det A = 22
  2. 2. det A = 15
  3. 3. det A = −58
  4. 4. c21 = −13
  5. 5. λ = 4
  6. 6. x = −1

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