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 =86−3−4

Find the determinant det A of the matrix A shown.

A = [8 6; −3 −4]
det A =
2.Easy
A =63−74

Find the determinant det A of the matrix A shown.

A = [6 3; −7 4]
det A =
3.Medium
A =−322−1−44−2−4−2

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

A = [−3 2 2; −1 −4 4; −2 −4 −2]
det A =
4.Medium
A =−4−432B =−413−5

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

A = [−4 −4; 3 2]B = [−4 1; 3 −5]
c12 =
5.Hard
A =2−22−6b =50

Solve the system 2x − 2y = 5 and 2x − 6y = 0. Find x.

2x − 2y = 52x − 6y = 0
x =
6.Hard
A =−5−356b =7−11

Solve the system −5x − 3y = 7 and 5x + 6y = −11. Find x.

−5x − 3y = 75x + 6y = −11
x =

Answer key

  1. 1. det A = −14
  2. 2. det A = 45
  3. 3. det A = −100
  4. 4. c12 = 16
  5. 5. x = 3.75
  6. 6. x = −0.6

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