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 =−1−7−90

Find the determinant det A of the matrix A shown.

A = [−1 −7; −9 0]
det A =
2.Easy
A =6−9−8−7

Find the determinant det A of the matrix A shown.

A = [6 −9; −8 −7]
det A =
3.Medium
A =−2−5252−3254

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

A = [−2 −5 2; 5 2 −3; 2 5 4]
det A =
4.Medium
A =36−2−3B =−1−2−3−4

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

A = [3 6; −2 −3]B = [−1 −2; −3 −4]
c21 =
5.Hard
A =63−1−6b =−4−9

Solve the system 6x + 3y = −4 and −x − 6y = −9. Find x.

6x + 3y = −4−x − 6y = −9
x =
6.Hard
A =531−2b =5−11

Solve the system 5x + 3y = 5 and x − 2y = −11. Find x.

5x + 3y = 5x − 2y = −11
x =

Answer key

  1. 1. det A = −63
  2. 2. det A = −114
  3. 3. det A = 126
  4. 4. c21 = 11
  5. 5. x = −1.545
  6. 6. x = −1.769

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