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 =−95−9−1

Find the determinant det A of the matrix A shown.

A = [−9 5; −9 −1]
det A =
2.Easy
A =−156−4

Find the determinant det A of the matrix A shown.

A = [−1 5; 6 −4]
det A =
3.Medium
A =−4−35−4−2−55−4−5

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

A = [−4 −3 5; −4 −2 −5; 5 −4 −5]
det A =
4.Medium
A =−4−100B =22−5−6

Let C = AB for the matrices shown. Find the entry c11 (row 1, column 1).

A = [−4 −1; 0 0]B = [2 2; −5 −6]
c11 =
5.Hard
A =−4−44−3b =99

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

−4x − 4y = 94x − 3y = 9
x =
6.Hard
A =6−21−5b =112

Solve the system 6x − 2y = 1 and x − 5y = 12. Find x.

6x − 2y = 1x − 5y = 12
x =

Answer key

  1. 1. det A = 54
  2. 2. det A = −26
  3. 3. det A = 305
  4. 4. c11 = −3
  5. 5. x = 0.3214
  6. 6. x = −0.6786

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