SOLVED: Linear AlgebraLet S= (s t, s, s - t) where s and t are real numbers .Find a basis for this subspace of R^3 and find the dimension ofS.

SOLVED:A subspace Y of a normed space X is said to be invariant under a linear operator T: X \longrightarrow X if T(Y) \subset Y. Show that an eigenspace of T is invariant under T. Give examples.

SOLVED:Suppose T \in \mathcal{L}(V) and U is a subspace of V. (a) Prove that if U \subset null T, then U is invariant under T. (b) Prove that if range T \subset U, then U is invariant under T.

SOLVED: For the subspace below, (a) find a basis for the subspace, and (b) state the dimensionp - 4q 2p 4r p, q,r in R 4q 2r 2p 4r

SOLVED:Find a basis and the dimension of the subspace W of V=𝐌2,2 spanned by A=[ 1 -5 -4 2 ], B=[ 1 1 -1 5 ], C=[ 2 -4 -5 7 ], D=[ 1 -7 -5 1 ]

SOLVED:(a) give a geometric description of, (b) find a basis for, and (c) determine the dimension of the subspace W of R^2 W={(0, t): t is a real number }