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 =9−5−4−7

Find the determinant det A of the matrix A shown.

A = [9 −5; −4 −7]
det A =
2.Easy
A =1−4−6−6

Find the determinant det A of the matrix A shown.

A = [1 −4; −6 −6]
det A =
3.Medium
A =−3030−5233−1

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

A = [−3 0 3; 0 −5 2; 3 3 −1]
det A =
4.Medium
A =306−2B =−35−21

Let C = AB for the matrices shown. Find the entry c22 (row 2, column 2).

A = [3 0; 6 −2]B = [−3 5; −2 1]
c22 =
5.Hard
A =−3−3−3−4b =6−4

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

−3x − 3y = 6−3x − 4y = −4
x =
6.Hard
A =−2166b =12−3

Solve the system −2x + y = 12 and 6x + 6y = −3. Find x.

−2x + y = 126x + 6y = −3
x =

Answer key

  1. 1. det A = −83
  2. 2. det A = −30
  3. 3. det A = 48
  4. 4. c22 = 28
  5. 5. x = −12
  6. 6. x = −4.167

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