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 =−73−4−6

Find the determinant det A of the matrix A shown.

A = [−7 3; −4 −6]
det A =
2.Easy
A =3−15−8

Find the determinant det A of the matrix A shown.

A = [3 −1; 5 −8]
det A =
3.Medium
A =400−2B =3−4−40

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

A = [4 0; 0 −2]B = [3 −4; −4 0]
c12 =
4.Medium
A =−150−2B =3−52−4

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

A = [−1 5; 0 −2]B = [3 −5; 2 −4]
c21 =
5.Hard
A =03−4−7

Find the larger eigenvalue λ of the matrix A shown.

A = [0 3; −4 −7]
λ =
6.Hard
A =−411−1b =−67

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

−4x + y = −6x − y = 7
x =

Answer key

  1. 1. det A = 54
  2. 2. det A = −19
  3. 3. c12 = −16
  4. 4. c21 = −4
  5. 5. λ = −3
  6. 6. x = −0.3333

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