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 =6369

Find the determinant det A of the matrix A shown.

A = [6 3; 6 9]
det A =
2.Easy
A =−5661

Find the determinant det A of the matrix A shown.

A = [−5 6; 6 1]
det A =
3.Medium
A =2−2−32−45−3−3−3

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

A = [2 −2 −3; 2 −4 5; −3 −3 −3]
det A =
4.Medium
A =51−1−1B =−44−2−6

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

A = [5 1; −1 −1]B = [−4 4; −2 −6]
c22 =
5.Hard
A =−1−4−35b =−7−10

Solve the system −x − 4y = −7 and −3x + 5y = −10. Find x.

−x − 4y = −7−3x + 5y = −10
x =
6.Hard
A =−31−53

Find the larger eigenvalue λ of the matrix A shown.

A = [−3 1; −5 3]
λ =

Answer key

  1. 1. det A = 36
  2. 2. det A = −41
  3. 3. det A = 126
  4. 4. c22 = 2
  5. 5. x = 4.412
  6. 6. λ = 2

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