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 =49−66

Find the determinant det A of the matrix A shown.

A = [4 9; −6 6]
det A =
2.Easy
A =−730−9

Find the determinant det A of the matrix A shown.

A = [−7 3; 0 −9]
det A =
3.Medium
A =−24−63B =6−5−66

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

A = [−2 4; −6 3]B = [6 −5; −6 6]
c11 =
4.Medium
A =3−5−232302−4

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

A = [3 −5 −2; 3 2 3; 0 2 −4]
det A =
5.Hard
A =−53−51b =012

Solve the system −5x + 3y = 0 and −5x + y = 12. Find x.

−5x + 3y = 0−5x + y = 12
x =
6.Hard
A =−3−36−5b =−46

Solve the system −3x − 3y = −4 and 6x − 5y = 6. Find x.

−3x − 3y = −46x − 5y = 6
x =

Answer key

  1. 1. det A = 78
  2. 2. det A = 63
  3. 3. c11 = −36
  4. 4. det A = −114
  5. 5. x = −3.6
  6. 6. x = 1.152

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