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 =9−95−3

Find the determinant det A of the matrix A shown.

A = [9 −9; 5 −3]
det A =
2.Easy
A =9−35−1

Find the determinant det A of the matrix A shown.

A = [9 −3; 5 −1]
det A =
3.Medium
A =12−52−2322−2

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

A = [1 2 −5; 2 −2 3; 2 2 −2]
det A =
4.Medium
A =25−3−6B =−33−12

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

A = [2 5; −3 −6]B = [−3 3; −1 2]
c11 =
5.Hard
A =−2−6−35b =1210

Solve the system −2x − 6y = 12 and −3x + 5y = 10. Find x.

−2x − 6y = 12−3x + 5y = 10
x =
6.Hard
A =−451−6b =1−1

Solve the system −4x + 5y = 1 and x − 6y = −1. Find x.

−4x + 5y = 1x − 6y = −1
x =

Answer key

  1. 1. det A = 18
  2. 2. det A = 6
  3. 3. det A = −22
  4. 4. c11 = −11
  5. 5. x = −4.286
  6. 6. x = −0.05263

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