所屬科目：研究所、轉學考(插大)◆工程數學
(c) Let A be m✖ n and let Pw be the orthogonal projection matrix for Col A. Then Ax = Pwb is consistent for each b .
(d) Let A1 and A2 be m✖ n matrices. If A1x = b1and A2x = b2 are consistent, then is consistent.
(e) Let V be a finite dimensional inner product space and let B be a basis for V. Then (f, g) = [f]B．[g]B, for any f,.
(g) Let (v1, v2,... , vn} be a basis for Rn. Let A be n x n. If ||Avill = llvil, for i=1.2. n, then A is orthogonal.
(h) Let T : be linear. Then there exist a pair of distinct vectors v1, V2 such that T(v1) = T(v2).
(i) Let Q and A be m x m and m x n matrices respectively, and . Let S1 and S2 be solution sets to Ax = b and QAx = Qb respectively. Then S1 is a subspace of S2.
3. (15%) Let P2 be the set of all polynomials with degree less than equal to 2. For any p1(x), p2(x) P2, their inner product is defined by Let W = {1, x} and p(x) = x2. Find the unique polynonialssuch that p(x)=q(x)+r(x).
(b) (4%) Find the conditional probability density function .
(d) (8%) Let Z = 3X + 2Y. Derive the moment generating function . You have to give the derivation, not just the an- swer.
(c) (8%) Let L =. Derive the probability mass finction of L. You have to give the derivation, not just the answer.
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is consistent. 
.
be linear. Then there exist a pair of distinct vectors v1, V2 
such that T(v1) = T(v2).
. Let S1 and
S2 be solution sets to Ax = b and QAx = Qb respectively. Then S1 is a subspace
of S2.
P2, their inner product is defined by
Let W = {1, x} and p(x) = x2. Find the unique polynonials
such that p(x)=q(x)+r(x).
.
. You have to give the derivation, not just the an- swer.
. Derive the probability mass finction of L. You have to give the derivation, not just the answer.