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 =4−1−77

Find the determinant det A of the matrix A shown.

A = [4 −1; −7 7]
det A =
2.Easy
A =−7−4−72

Find the determinant det A of the matrix A shown.

A = [−7 −4; −7 2]
det A =
3.Medium
A =10−34B =−6362

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

A = [1 0; −3 4]B = [−6 3; 6 2]
c12 =
4.Medium
A =−42−3−11−313−1

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

A = [−4 2 −3; −1 1 −3; 1 3 −1]
det A =
5.Hard
A =−1131

Find the larger eigenvalue λ of the matrix A shown.

A = [−1 1; 3 1]
λ =
6.Hard
A =−62−2−2b =−412

Solve the system −6x + 2y = −4 and −2x − 2y = 12. Find x.

−6x + 2y = −4−2x − 2y = 12
x =

Answer key

  1. 1. det A = 21
  2. 2. det A = −42
  3. 3. c12 = 3
  4. 4. det A = −28
  5. 5. λ = 2
  6. 6. x = −1

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