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 =2527

Find the determinant det A of the matrix A shown.

A = [2 5; 2 7]
det A =
2.Easy
A =−44−40

Find the determinant det A of the matrix A shown.

A = [−4 4; −4 0]
det A =
3.Medium
A =−1−53−3−3−4−45−1

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

A = [−1 −5 3; −3 −3 −4; −4 5 −1]
det A =
4.Medium
A =−404−1B =−56−21

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

A = [−4 0; 4 −1]B = [−5 6; −2 1]
c21 =
5.Hard
A =−5−4−1−3b =10−8

Solve the system −5x − 4y = 10 and −x − 3y = −8. Find x.

−5x − 4y = 10−x − 3y = −8
x =
6.Hard
A =−2−413b =10−2

Solve the system −2x − 4y = 10 and x + 3y = −2. Find x.

−2x − 4y = 10x + 3y = −2
x =

Answer key

  1. 1. det A = 4
  2. 2. det A = 16
  3. 3. det A = −169
  4. 4. c21 = −18
  5. 5. x = −5.636
  6. 6. x = −11

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