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 =−3−2−44

Find the determinant det A of the matrix A shown.

A = [−3 −2; −4 4]
det A =
2.Easy
A =5−8−88

Find the determinant det A of the matrix A shown.

A = [5 −8; −8 8]
det A =
3.Medium
A =−4−5−14B =−3−405

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

A = [−4 −5; −1 4]B = [−3 −4; 0 5]
c21 =
4.Medium
A =−1−510−2−3−53−5

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

A = [−1 −5 1; 0 −2 −3; −5 3 −5]
det A =
5.Hard
A =2184

Find the larger eigenvalue λ of the matrix A shown.

A = [2 1; 8 4]
λ =
6.Hard
A =32−4−6b =−73

Solve the system 3x + 2y = −7 and −4x − 6y = 3. Find x.

3x + 2y = −7−4x − 6y = 3
x =

Answer key

  1. 1. det A = −20
  2. 2. det A = −24
  3. 3. c21 = 3
  4. 4. det A = −104
  5. 5. λ = 6
  6. 6. x = −3.6

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