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 =98−2−5

Find the determinant det A of the matrix A shown.

A = [9 8; −2 −5]
det A =
2.Easy
A =6−8−8−7

Find the determinant det A of the matrix A shown.

A = [6 −8; −8 −7]
det A =
3.Medium
A =−3−4−3−10−2−3−4−4

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

A = [−3 −4 −3; −1 0 −2; −3 −4 −4]
det A =
4.Medium
A =625−6B =−556−4

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

A = [6 2; 5 −6]B = [−5 5; 6 −4]
c12 =
5.Hard
A =1345b =−18

Solve the system x + 3y = −1 and 4x + 5y = 8. Find x.

x + 3y = −14x + 5y = 8
x =
6.Hard
A =−1151b =−4−11

Solve the system −x + y = −4 and 5x + y = −11. Find x.

−x + y = −45x + y = −11
x =

Answer key

  1. 1. det A = −29
  2. 2. det A = −106
  3. 3. det A = 4
  4. 4. c12 = 22
  5. 5. x = 4.143
  6. 6. x = −1.167

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