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 =2209

Find the determinant det A of the matrix A shown.

A = [2 2; 0 9]
det A =
2.Easy
A =5−3−5−4

Find the determinant det A of the matrix A shown.

A = [5 −3; −5 −4]
det A =
3.Medium
A =−51−5−2B =0−32−3

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

A = [−5 1; −5 −2]B = [0 −3; 2 −3]
c21 =
4.Medium
A =−65−46B =−3222

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

A = [−6 5; −4 6]B = [−3 2; 2 2]
c11 =
5.Hard
A =−4−51−3b =3−9

Solve the system −4x − 5y = 3 and x − 3y = −9. Find x.

−4x − 5y = 3x − 3y = −9
x =
6.Hard
A =23−1−2

Find the larger eigenvalue λ of the matrix A shown.

A = [2 3; −1 −2]
λ =

Answer key

  1. 1. det A = 18
  2. 2. det A = −35
  3. 3. c21 = −4
  4. 4. c11 = 28
  5. 5. x = −3.176
  6. 6. λ = 1

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