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 =14−75

Find the determinant det A of the matrix A shown.

A = [1 4; −7 5]
det A =
2.Easy
A =45−30

Find the determinant det A of the matrix A shown.

A = [4 5; −3 0]
det A =
3.Medium
A =6105B =−4−21−6

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

A = [6 1; 0 5]B = [−4 −2; 1 −6]
c21 =
4.Medium
A =2−5331−414−2

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

A = [2 −5 3; 3 1 −4; 1 4 −2]
det A =
5.Hard
A =411−1b =−4−8

Solve the system 4x + y = −4 and x − y = −8. Find x.

4x + y = −4x − y = −8
x =
6.Hard
A =−5−2−6−3b =57

Solve the system −5x − 2y = 5 and −6x − 3y = 7. Find x.

−5x − 2y = 5−6x − 3y = 7
x =

Answer key

  1. 1. det A = 33
  2. 2. det A = 15
  3. 3. c21 = 5
  4. 4. det A = 51
  5. 5. x = −2.4
  6. 6. x = −0.3333

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