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 =−2−67−5

Find the determinant det A of the matrix A shown.

A = [−2 −6; 7 −5]
det A =
2.Easy
A =−2556

Find the determinant det A of the matrix A shown.

A = [−2 5; 5 6]
det A =
3.Medium
A =4−51−3−2−2−2−55

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

A = [4 −5 1; −3 −2 −2; −2 −5 5]
det A =
4.Medium
A =5464B =−413−5

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

A = [5 4; 6 4]B = [−4 1; 3 −5]
c22 =
5.Hard
A =−6−12−4b =61

Solve the system −6x − y = 6 and 2x − 4y = 1. Find x.

−6x − y = 62x − 4y = 1
x =
6.Hard
A =−1−126b =101

Solve the system −x − y = 10 and 2x + 6y = 1. Find x.

−x − y = 102x + 6y = 1
x =

Answer key

  1. 1. det A = 52
  2. 2. det A = −37
  3. 3. det A = −164
  4. 4. c22 = −14
  5. 5. x = −0.8846
  6. 6. x = −15.25

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