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 =−979−5

Find the determinant det A of the matrix A shown.

A = [−9 7; 9 −5]
det A =
2.Easy
A =8−4−76

Find the determinant det A of the matrix A shown.

A = [8 −4; −7 6]
det A =
3.Medium
A =−4−4−50B =153−1

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

A = [−4 −4; −5 0]B = [1 5; 3 −1]
c21 =
4.Medium
A =−4010B =1−2−23

Let C = AB for the matrices shown. Find the entry c11 (row 1, column 1).

A = [−4 0; 1 0]B = [1 −2; −2 3]
c11 =
5.Hard
A =3−2−50

Find the larger eigenvalue λ of the matrix A shown.

A = [3 −2; −5 0]
λ =
6.Hard
A =6522b =8−2

Solve the system 6x + 5y = 8 and 2x + 2y = −2. Find x.

6x + 5y = 82x + 2y = −2
x =

Answer key

  1. 1. det A = −18
  2. 2. det A = 20
  3. 3. c21 = −5
  4. 4. c11 = −4
  5. 5. λ = 5
  6. 6. x = 13

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