4. Show that the norm on (° given by I| (21, ..., In...) |lo= sup{|7;| : j =1,2, ...} %3D can not be given by a scalar product.

Q: A vector y in Rn can also be viewed as an n × 1matrix Y = (y). Show that ||Y||2 = ||y||2

A:

Q: 4. Check that the following are vector spaces: (a) RN. 55 / 600 (b) CN. (c) C(N), where 2 is a…

A: A non-empty set V, +, · is said to be a vector space over a field F together with operations of…

Q: 2. Let x = (1, 1, 1, 1)" and y = (8, 2, 2, 0)". (a) Determine the angle 0 between x and y. (b) Find…

A:

Q: 56. Which vector spaces are isomorphic to R6? (c) C[0, 6] (f) C'[-3, 3] (a) M23 (b) Ро (d) M6,1 (e)…

A:

Q: Find the condition for the points (a, 0). (h, k){0,b) when ab = 0 to be collinear.

A: Find the condition for the given points to be collinear.

Q: Let x=x= and y=y= Find the dot product of xx and yy.     x⋅y=x⋅y

A: Given:x=9, 0y=-4, -2Dot product:A=ax ,ay  B=bx ,byAB=axbx,+ay,by

Q: Let a= and b= Show that there are scalars s and t so that sa+tb=. s = ? t = ?

A: a=-5,0,-3 and b=4,0,2sa+tb=27,0,15

Q: s an inner product space, where (a, 5) = 4 – 5i.

A:

Q: ^2

A:

Q: Q2/ Show that {1,cosx, sinx,cos2x, sinx,...} Form an orthogonal set on [-Tt,t] *

A: A set of vector B is orthogonal if every vector in the set is orthogonal. Therefore, the dot product…

Q: Assume that span(R) = RS. What is the payoff of the portfolio Zg = R¹ (RR¹) −¹ es when es € R$ is a…

A: Given: The portfolio, zs=RTRRT-1esTo find: The payoff of the portfolio zs.

Q: Q4) Consider the space (X.Tu) and let A = [0,2) U (3) U (4,7). Find d(A), A, Aº, ext(A) and b(A).

A:

Q: Show that in 3D space, (a) k EijkEpqk = δip&jq – διαδjp

A: Note:  Since you have posted multiple questions, we will solve first question for you. Kindly repost…

Q: For (a, B) E R?, define a function (-, -) : R² × R? → R by setting arr' + xy + Yx' + Byy' . 1. Find…

A:

Q: (d) Passing through the point (0, 1, 2), perpendicular to the line L and intersects L. L(xo. v) =…

A:

Q: Take a defineal a transformation. by OIYE Vectors in the w(x)- cCKed where c and d EU clidean plane…

A: In euclidean plane, d(x,y) = |x-y| ∀x,y∈ℝ.

Q: Let X₁ = [1 3 −1 1]²‚×₂ = [3 −1 3 1]′, and x3 = [-1 2 −3 1]. Is b = T an element of span{X₁, X₂,…

A: No, we can write it.

Q: - In(a°y*) + x2 Consider z as a function of the variables x, y which is denoted by z and let P(1,-1)…

A:

Q: Let à = ст -5' -4 Find ||a, the norm of a.

A: The norm of a vector is simply the square root of the sum of each component squared.Explanation:

Q: The solution of the following Bernoulli's equation xy' + 2y = x¹(cos x) y² is

A: The correct answer is not given in options.The solution with the correct answer is given as

Q: B. Is C a real vector space? Explain.

A:

Q: Use Green's Theorem to evaluate $. xydx + x²y³dy, where C is the triangle with vertices (0,0), (1,0)…

A: Consider the provided question, ∮cxydx+x2y3dy,     where c is the triangle with vertices 0,0, 1,0…