Finding the Determinant of a 2x2 Matrix

[JFonseka]

Homework Statement

A 2 x 2 matrix B satisfies

B (3 1)^{T} = B (5 2)^{T}

What is det (B) ? Give a reason

Homework Equations

None really

The Attempt at a Solution

I really have no idea how to start solving this. Does it involve inversing?

 

[Dick]

You are saying Bx=By. What's B(x-y)? Does that give you a hint?

 

[JFonseka]

So, It's B(-2 -1)^{T}

I don't get it though. That doesn't look like a determinant.

 

[Dick]

It's also equal to zero since Bx=By. It's not a determinant. But Bz=0 where z is a nonzero vector. What can that tell you about the determinant of B?

 

[JFonseka]

That the determinant is 0 ?

 

[Dick]

Yessssss.

 

[JFonseka]

How do we know B(x) = 0?

 

[JFonseka]

Ah nvm I see.

Thanks for the help