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 =35−7−8

Find the determinant det A of the matrix A shown.

A = [3 5; −7 −8]
det A =
2.Easy
A =71−2−9

Find the determinant det A of the matrix A shown.

A = [7 1; −2 −9]
det A =
3.Medium
A =3−3−142−15−31

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

A = [3 −3 −1; 4 2 −1; 5 −3 1]
det A =
4.Medium
A =−16−50B =2−454

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

A = [−1 6; −5 0]B = [2 −4; 5 4]
c21 =
5.Hard
A =1−4−3−4b =−83

Solve the system x − 4y = −8 and −3x − 4y = 3. Find x.

x − 4y = −8−3x − 4y = 3
x =
6.Hard
A =−6165b =12−12

Solve the system −6x + y = 12 and 6x + 5y = −12. Find x.

−6x + y = 126x + 5y = −12
x =

Answer key

  1. 1. det A = 11
  2. 2. det A = −61
  3. 3. det A = 46
  4. 4. c21 = −10
  5. 5. x = −2.75
  6. 6. x = −2

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