14. Fix a non-zero vector n R". Lot L : Rn → Rn be the linear mapping defined by L()-2 proj(T), f...
14. Fix a non-zero vector i e R". Let L: R" → R" be the linear mapping defined by L(7) = – 2 proj„(7), for all a E R" (a) Show that if je R", such that j + ð and j ·ñ = 0, then j is an eigenvector of L. What is its eigenvalue? (b) Show that i is an eigenvector of L. What is its eigenvalue? (c) What are the algebraic and geometric multiplicities of all eigenvalues...
LetM: R2 + R’ be a linear mapping defined by [21 - g] T+2g M L _V_ J What is the standard matrix? 0[2 -1] .11 2 11 ܂ : ܂1 Oro - 7 ܘ 7 0 ܗ ܗ 7 D[ ܗ ܗ 7
Let M be a 8:27 AM right R-module, N be an (R,T)-bimodule, and L be a left T-module. Let e: (MN)* L M R (NB, L) be given by e (moon, e) = m (nol). Let m.con, mone MORN, and lEl. Prove e (lm, BR.) + (m₂ Ore), d)= e(m, on, d) + (mon, e). This is the proof I'm working on. I need to show the map I've defined (and which is defined towards the middle of the proof)...
Let TRm → Rn be a linear transformation, and let p be a vector and S a set in R Show that the image of p + S under T is the translated set T(p) + T(S) n R What would be the first step in translating p+ S? OA. Rewrite p+ S so that it does not use sets. O B. Rewrite p+S so that it does not use vectors O c. Rewrite p + S as a difference...
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Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that the cardinality of the set A bounded by m(m1)/2. e [0, 1]: f(x) > 1/m) is c) Given m E N construct a partition P such that U(f, Pm)2/m. d) Show that f is integrable and compute Jo...