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 =5−49−1

Find the determinant det A of the matrix A shown.

A = [5 −4; 9 −1]
det A =
2.Easy
A =−920−4

Find the determinant det A of the matrix A shown.

A = [−9 2; 0 −4]
det A =
3.Medium
A =3−544B =61−3−2

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

A = [3 −5; 4 4]B = [6 1; −3 −2]
c11 =
4.Medium
A =5−1−23155−52

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

A = [5 −1 −2; 3 1 5; 5 −5 2]
det A =
5.Hard
A =−2−225b =−32

Solve the system −2x − 2y = −3 and 2x + 5y = 2. Find x.

−2x − 2y = −32x + 5y = 2
x =
6.Hard
A =−1−64−4b =7−2

Solve the system −x − 6y = 7 and 4x − 4y = −2. Find x.

−x − 6y = 74x − 4y = −2
x =

Answer key

  1. 1. det A = 31
  2. 2. det A = 36
  3. 3. c11 = 33
  4. 4. det A = 156
  5. 5. x = 1.833
  6. 6. x = −1.429

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