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 =4241

Find the determinant det A of the matrix A shown.

A = [4 2; 4 1]
det A =
2.Easy
A =7067

Find the determinant det A of the matrix A shown.

A = [7 0; 6 7]
det A =
3.Medium
A =−21−4−4−40−1−12

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

A = [−2 1 −4; −4 −4 0; −1 −1 2]
det A =
4.Medium
A =−134−3B =−160−3

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

A = [−1 3; 4 −3]B = [−1 6; 0 −3]
c12 =
5.Hard
A =−5−3−22b =−33

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

−5x − 3y = −3−2x + 2y = 3
x =
6.Hard
A =−53−65b =−126

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

−5x + 3y = −12−6x + 5y = 6
x =

Answer key

  1. 1. det A = −4
  2. 2. det A = 49
  3. 3. det A = 24
  4. 4. c12 = −15
  5. 5. x = −0.1875
  6. 6. x = 11.14

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