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 =−6−417

Find the determinant det A of the matrix A shown.

A = [−6 −4; 1 7]
det A =
2.Easy
A =−2−6−10

Find the determinant det A of the matrix A shown.

A = [−2 −6; −1 0]
det A =
3.Medium
A =−4−41−4345−54

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

A = [−4 −4 1; −4 3 4; 5 −5 4]
det A =
4.Medium
A =645−6B =−3−2−63

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

A = [6 4; 5 −6]B = [−3 −2; −6 3]
c11 =
5.Hard
A =−613−4b =−73

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

−6x + y = −73x − 4y = 3
x =
6.Hard
A =66−5−7

Find the larger eigenvalue λ of the matrix A shown.

A = [6 6; −5 −7]
λ =

Answer key

  1. 1. det A = −38
  2. 2. det A = −6
  3. 3. det A = −267
  4. 4. c11 = −42
  5. 5. x = 1.19
  6. 6. λ = 3

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