N 1. Let X := RN be the N-dimensional real vector space with the usual norm, that is, ||x|| := / x² + ··· + x²/√ for x = (x1,...,xN). For each x, y = RN, put T(x)(y) := Σ\/\±1x(k)y(k). Show that T is an isometric isomorphism from RN onto its dual space.

Q: Find the domain of the vector function r(t) = (t, √t — 4, √5 — t Domain: {t | <t< }

A:

Q: Consider the line V = {(t,t + 1) |t € R} in R. Let V be the real vector space with vector addition e…

A:

Q: Determine whether the vector functions, x1(t)= [ et ]           [ -et ] and x2(t)= [ et ]…

A:

Q: 1. Let f: R" → R be the function f(x) = cx+b for some fixed vector c ER" and scalar b. Show that f…

A:

Q: If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is…

A: Here we have to find single vector x whose image under T is b.

Q: use linear functions. The ABC Car Rental uses the function f (x) = 100 for any daily use of a car up…

A: Driving More than 200 miles per day.   ABC uses the function g(x) =100+0.25(x-200)toTo determine the…

Q: 2s Let H be the set of all vectors of the form Find a vector v in R' such that H span {i}. -s S

A: Spanning set of H

Q: 5. Let ū = (-1,3, 2) and i = (1, 1, -1). Find all vectors x' that satisfy u x i = v.

A:

Q: Find the domain of the vector functions, r(t), listed below. You may use "-INF" for -∞o and use…

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: 1. Let V = C[-2, 2], the vector space of continuous functions on the closed interval [-2, 2). Let f,…

A: We can just multiply h and k and integrate  Then after simplifying we are getting answer

Q: (a) Find the best approximation to ✅ by a vector of W. (b) Write as the sum of a vector in W and a…

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…