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 =2−293

Find the determinant det A of the matrix A shown.

A = [2 −2; 9 3]
det A =
2.Easy
A =−5−66−6

Find the determinant det A of the matrix A shown.

A = [−5 −6; 6 −6]
det A =
3.Medium
A =−2045533−4−4

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

A = [−2 0 4; 5 5 3; 3 −4 −4]
det A =
4.Medium
A =2−3−10B =1−404

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

A = [2 −3; −1 0]B = [1 −4; 0 4]
c21 =
5.Hard
A =−5−6−31b =−109

Solve the system −5x − 6y = −10 and −3x + y = 9. Find x.

−5x − 6y = −10−3x + y = 9
x =
6.Hard
A =−4−3−66b =11−4

Solve the system −4x − 3y = 11 and −6x + 6y = −4. Find x.

−4x − 3y = 11−6x + 6y = −4
x =

Answer key

  1. 1. det A = 24
  2. 2. det A = 66
  3. 3. det A = −124
  4. 4. c21 = −1
  5. 5. x = −1.913
  6. 6. x = −1.286

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