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 =−1−688

Find the determinant det A of the matrix A shown.

A = [−1 −6; 8 8]
det A =
2.Easy
A =3−5−84

Find the determinant det A of the matrix A shown.

A = [3 −5; −8 4]
det A =
3.Medium
A =−4−431−4−25−31

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

A = [−4 −4 3; 1 −4 −2; 5 −3 1]
det A =
4.Medium
A =6121B =244−6

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

A = [6 1; 2 1]B = [2 4; 4 −6]
c22 =
5.Hard
A =−6−6−35b =3−6

Solve the system −6x − 6y = 3 and −3x + 5y = −6. Find x.

−6x − 6y = 3−3x + 5y = −6
x =
6.Hard
A =−2−5−1−4b =−712

Solve the system −2x − 5y = −7 and −x − 4y = 12. Find x.

−2x − 5y = −7−x − 4y = 12
x =

Answer key

  1. 1. det A = 40
  2. 2. det A = −28
  3. 3. det A = 135
  4. 4. c22 = 2
  5. 5. x = 0.4375
  6. 6. x = 29.33

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