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 =−39−11

Find the determinant det A of the matrix A shown.

A = [−3 9; −1 1]
det A =
2.Easy
A =330−9

Find the determinant det A of the matrix A shown.

A = [3 3; 0 −9]
det A =
3.Medium
A =1−432−32−5−4−4

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

A = [1 −4 3; 2 −3 2; −5 −4 −4]
det A =
4.Medium
A =−1−53−3B =1−20−1

Let C = AB for the matrices shown. Find the entry c12 (row 1, column 2).

A = [−1 −5; 3 −3]B = [1 −2; 0 −1]
c12 =
5.Hard
A =4311b =−9−6

Solve the system 4x + 3y = −9 and x + y = −6. Find x.

4x + 3y = −9x + y = −6
x =
6.Hard
A =1512b =1011

Solve the system x + 5y = 10 and x + 2y = 11. Find x.

x + 5y = 10x + 2y = 11
x =

Answer key

  1. 1. det A = 6
  2. 2. det A = −27
  3. 3. det A = −41
  4. 4. c12 = 7
  5. 5. x = 9
  6. 6. x = 11.67

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