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 =99−95

Find the determinant det A of the matrix A shown.

A = [9 9; −9 5]
det A =
2.Easy
A =−4−23−7

Find the determinant det A of the matrix A shown.

A = [−4 −2; 3 −7]
det A =
3.Medium
A =−2−40−50−4−4−52

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

A = [−2 −4 0; −5 0 −4; −4 −5 2]
det A =
4.Medium
A =3−23−5B =−50−50

Let C = AB for the matrices shown. Find the entry c21 (row 2, column 1).

A = [3 −2; 3 −5]B = [−5 0; −5 0]
c21 =
5.Hard
A =13−2−3b =−12−12

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

x + 3y = −12−2x − 3y = −12
x =
6.Hard
A =−3−4−6−4b =−106

Solve the system −3x − 4y = −10 and −6x − 4y = 6. Find x.

−3x − 4y = −10−6x − 4y = 6
x =

Answer key

  1. 1. det A = 126
  2. 2. det A = 34
  3. 3. det A = −64
  4. 4. c21 = 10
  5. 5. x = 24
  6. 6. x = −5.333

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