(10) Recall that for a unit vector ū= in R2, the matrix P = ūūt represents...
(5) (10") Recall that for a unit vector ū in R, the matrix P = ūū represents the projection on ü. (a) Are there values a and b such that P is a SPD matrix? Explain. (b) Orthogonally diagonalize P. (c) Orthogonally diagonalize the reflection matrix L = 2P-I
10') Determine the range of a so that the quadratic form Q(x, y, z) = a(r+y+z)+2xy-2yz+2zx positive definite.
Theorem. Consider the quadratic form Q(x) = Ar where A is anxn symmetric matrix and A, and denote the largest and smallest eigenvalues of A, respectively. Then max Q(x) = 2 = max Q() = 1 and Q0.) = 1, where is any unit eige vector corre sponding to ii) in (r) and QU.) where is any unit eigen vector corresponding to do 1. - Find max Q(x) and min Q(x). 1) Q(1) = 3x + 43273 +673 ii) Q(z)...