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 =−6−6−8−9

Find the determinant det A of the matrix A shown.

A = [−6 −6; −8 −9]
det A =
2.Easy
A =−5−608

Find the determinant det A of the matrix A shown.

A = [−5 −6; 0 8]
det A =
3.Medium
A =−5416B =−5−633

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

A = [−5 4; 1 6]B = [−5 −6; 3 3]
c21 =
4.Medium
A =5−25−252525

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

A = [5 −2 5; −2 5 2; 5 2 5]
det A =
5.Hard
A =−255−4b =−4−3

Solve the system −2x + 5y = −4 and 5x − 4y = −3. Find x.

−2x + 5y = −45x − 4y = −3
x =
6.Hard
A =36−1−3b =125

Solve the system 3x + 6y = 12 and −x − 3y = 5. Find x.

3x + 6y = 12−x − 3y = 5
x =

Answer key

  1. 1. det A = 6
  2. 2. det A = −40
  3. 3. c21 = 13
  4. 4. det A = −80
  5. 5. x = −1.824
  6. 6. x = 22

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