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 =−3756

Find the determinant det A of the matrix A shown.

A = [−3 7; 5 6]
det A =
2.Easy
A =5−191

Find the determinant det A of the matrix A shown.

A = [5 −1; 9 1]
det A =
3.Medium
A =−250−152−1−44

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

A = [−2 5 0; −1 5 2; −1 −4 4]
det A =
4.Medium
A =−4−43−6B =−1−1−3−3

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

A = [−4 −4; 3 −6]B = [−1 −1; −3 −3]
c21 =
5.Hard
A =652−2b =6−1

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

6x + 5y = 62x − 2y = −1
x =
6.Hard
A =−6−3−21b =−72

Solve the system −6x − 3y = −7 and −2x + y = 2. Find x.

−6x − 3y = −7−2x + y = 2
x =

Answer key

  1. 1. det A = −53
  2. 2. det A = 14
  3. 3. det A = −46
  4. 4. c21 = 15
  5. 5. x = 0.3182
  6. 6. x = 0.08333

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