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 =7−418

Find the determinant det A of the matrix A shown.

A = [7 −4; 1 8]
det A =
2.Easy
A =9−9−2−5

Find the determinant det A of the matrix A shown.

A = [9 −9; −2 −5]
det A =
3.Medium
A =124554121

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

A = [1 2 4; 5 5 4; 1 2 1]
det A =
4.Medium
A =0−4−44B =2−531

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

A = [0 −4; −4 4]B = [2 −5; 3 1]
c12 =
5.Hard
A =−4−1−1−2b =4−6

Solve the system −4x − y = 4 and −x − 2y = −6. Find x.

−4x − y = 4−x − 2y = −6
x =
6.Hard
A =5−241b =−28

Solve the system 5x − 2y = −2 and 4x + y = 8. Find x.

5x − 2y = −24x + y = 8
x =

Answer key

  1. 1. det A = 60
  2. 2. det A = −63
  3. 3. det A = 15
  4. 4. c12 = −4
  5. 5. x = −2
  6. 6. x = 1.077

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