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 =−7−7−47

Find the determinant det A of the matrix A shown.

A = [−7 −7; −4 7]
det A =
2.Easy
A =707−3

Find the determinant det A of the matrix A shown.

A = [7 0; 7 −3]
det A =
3.Medium
A =4−1−4−3−512−1−4

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

A = [4 −1 −4; −3 −5 1; 2 −1 −4]
det A =
4.Medium
A =4−441B =242−3

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

A = [4 −4; 4 1]B = [2 4; 2 −3]
c21 =
5.Hard
A =−42−4−5b =15

Solve the system −4x + 2y = 1 and −4x − 5y = 5. Find x.

−4x + 2y = 1−4x − 5y = 5
x =
6.Hard
A =−311−3

Find the larger eigenvalue λ of the matrix A shown.

A = [−3 1; 1 −3]
λ =

Answer key

  1. 1. det A = −77
  2. 2. det A = −21
  3. 3. det A = 42
  4. 4. c21 = 10
  5. 5. x = −0.5357
  6. 6. λ = −2

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