On Nov 4, 9:48 pm, G Patel <gaya.pa...@gmail.com> wrote: > On Nov 4, 9:56 pm, G Patel <gaya.pa...@gmail.com> wrote: > > > true or false.... eigenvalues of A are same as eigenvalues of kA > > (because if v is eigenvector for A, then kv is eigenvector for kA) > > if c is eigenvalue of A, then Ax = cx for nonzero x, multiply both > sides by nonzero scalar k: (kA)x = c(kx) , thus c is also eigenvalue > of kA?
An eigenvalue of A is a scalar c such that there exists a nonzero vector x for which Ax=cx.
Note that the vector on the left side of "Ax=cx" is the *same* as the vector on the right side of "Ax=cx".
Question: is the vector on the left side of your "(kA)x = c(kx)" the same as the vector on your right hand side?
And to put it even more plainly, *again*:
What are the eigenvalues of, say, the identity matrix?
What are the eigenvalues of k times the identity?
PS: You are utterly confused; go talk to your professor because you are just not getting this.