Show that det(I-xy'T)= 1-y'T x

[kutaybulbul]

Need Help Please!

I am very much in need of your help. I have a question saying:

Let x,y E R. Show that det(I-xy'T)= 1-y'T x

y'T is transpose of y and I is identity matrix.

Actually I don't know how to solve something like det( A-B). What am I going to do when there is addition or subtraction in the determinant.

Thanks for your response.

 

[quasar987]

Well for some square matrix M, you know how to calculate $\det(M)$, right? And for two nxn square matrices A and B, A-B is an nxn matrix C, true again? Then calculating $\det(A-B)$ is no different than calculating $\det(C)$.

 

[kutaybulbul]

So is this so simple wov thank you very much I think I can handle the rest.

 

[HallsofIvy]

In future it might be a good idea not to say things like
"Let x,y E R" and then assert that they are matrices!