Linear Algebra a What is det A b What is det5A c If B is a

Linear Algebra:

a) What is det A ?

b) What is det(5A) ?

c) If B is an arbitrary 2 × 2 matrix, what is the ratio det(5B)/ det(B) ? Think how the area of a parallelogram scales if all its edges are multiplied by a factor of 5.

d) If B is an arbitrary 3 × 3 matrix, what is the ratio det(5B)/ det(B)? Think how the volume of a parallelepiped scales if all its edges are multiplied by 5.

Solution

SOLUTIONA:

det A=ad-bc=2(4)-3(3)=8-9=-1

SOLUTIONB:

det(5A)=5² (detA)

=25(-1)

from above a bit

det(5A) = --25

SolutionC:

ratio det(5B)/ det(B)=5² detB/detB=25

SolutionD

ratio det(5B)/ det(B)=5² detB/detB=25