Let CE Rxn be a matrix such that xCx>0 for all nonzero vectors x ER". Prove that C is nonsingular.

Let V be the set of all 2× 3 matrices. Verify that V is a vector space.

Let CER" be a matrix such that xCx > 0 for all nonzero vectors & Prove that for k= 1,...,n, the leading principal submatrix C, satisfies y all nonzero vectors y ERK. Consequently, each C is nonsingular. R" Cky > 0 for

Let T be a linear operator defined on P3 by T(a0+a1x+a2x^2)=a0+a1(x-1)+a2(x-1)^2. The third row of the matrix associated with T with respect to base 1, x, x^2 is: a) (0,0,1) b) other response c) (1,-2,1) d) (1,0,0) e) (-1,1,0)