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 =36−6−7

Find the determinant det A of the matrix A shown.

A = [3 6; −6 −7]
det A =
2.Easy
A =−60−32

Find the determinant det A of the matrix A shown.

A = [−6 0; −3 2]
det A =
3.Medium
A =−513−3553−12

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

A = [−5 1 3; −3 5 5; 3 −1 2]
det A =
4.Medium
A =6−6−23B =2−4−64

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

A = [6 −6; −2 3]B = [2 −4; −6 4]
c22 =
5.Hard
A =3−15−3

Find the larger eigenvalue λ of the matrix A shown.

A = [3 −1; 5 −3]
λ =
6.Hard
A =61−66b =8−2

Solve the system 6x + y = 8 and −6x + 6y = −2. Find x.

6x + y = 8−6x + 6y = −2
x =

Answer key

  1. 1. det A = 15
  2. 2. det A = −12
  3. 3. det A = −90
  4. 4. c22 = 20
  5. 5. λ = 2
  6. 6. x = 1.19

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