Let M be an n xn matrix over R given by M = D+u®v" where D is a diagonal matrix over R and u, v are column vectors in R". The eigenvalue equation is given by Mx = (D+u®v)x= Ax. Assume that u;v; # 0. Show that リ=1 0 = 1+ r- *p). k=1

Please help me solve this. I got to all three eigens are equal to zero by doing subtraction of 5(first equation)-(third equation) and 3(first equation)-(second equation) and then solced out for my "a" "b" and "c" values. where did I go wrong here?? only HANDWRITTEN answer needed ( NOT TYPED)

For the matrix A , there is an invertible matrix P such that P^(−1)*AP = D, where D is a diagonal matrix with the eigenvalues of A on the diagonal.  Calculate the matrix product P^(-1)*AP

Suppose A + u are distinct eigenvalues of A, with corresponding eigenvectors u and v. (Au)™v = Au" v O pu"v V O du7v (Check ALL that apply) uv = are column vectors corresponding to the vectors u, v, then u'v is a Prove your result. Suggestion: If u, matrix whose entry is i · v.