Please help me in last 2 steps how c became 0 in u vector

[Ar8983]

Please help me in last 2 steps how c became 0 in u vector

 

[Cubist]

The final, "So let u=...", seems equivalent to saying...

So let c=0, b=a1

I think there may be other possible u matrices that satisfy the ker(T) requirement (whatever that may be I've never seen ker() before ). Perhaps these chosen values are appropriate for some "greater good" within this document, or maybe the values were just chosen simply because the resultant matrix looks fairly simple/ easy to work with.

 

[pka]

(T)he ker(T) requirement (whatever that may be I've never seen ker() before ).

If [imath]V[/imath] is a vector space and [imath]T[/imath] is a linear transformation on [imath]V[/imath] then [imath]\ker(T)=\{v\in V: T(v)={\bf 0}\}[/imath]