Consider the set V = {(x, y) = R² : x+y=1}. on this set defined in the following way: (x2, y2) = (x₁ + x₂ − 1, y₁ + y2) - k⋆ (x, y) (kxk+1, ky) Show that the set V equipped with operations and Let and be operations (x₁, y₁) = for kER. is a real vector space.

Q: Let F= R and V = R*. Let W, = {(x1,x2,X3,X4) € R* : x1 – x2 + X3 – x4 = 0 and x1 +x2 = 0}, W2 =…

A:

Q: Let B={(1,-2,0,-1), (0,1,0,3), (1,2,1.0)], and x=(4,3,-2,-5) Find [x]B Give your answer in the form…

A: B=1, -2, 0, -1, 0, 1, 0, 3, 1, 2, 1, 0x=4, 3, -2, -5

Q: Let u = (2,6, 4) and 7 = (-1, -2, - 7). Compute the following: ū. v = vu - ||||²

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: 13. Find the intersection of [x, y, z)=[-8,-3,-5]+[1,2,-1] and [x. v.]=[1.9,4]+s[2,1,7].

A: We can find the intersection of the curve .

Q: Find 4rye®y? dA, where R [0, 1] × [0, 2]. R

A: The objective is to find the double integration where  R=[0,1]×[0,2]

Q: Submit through Canvas as indicated. T u = (2,-5) and v= −3i+7j

A:

Q: Show that X is Hausdorff if and only if the diagonal △ = {(x, x)|x ∈ X} is closed in X × X.

A:

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

A:

Q: Let x) 4 and gx)-x-3. Find the foilowing lock

A: To find the following expressions

Q: Let u = Compute the following: ū• v = (1, −5, −1) and v = (-5,2,0). v.u ||ū|| ² - 3 (u.v) (-3ū) v =…

A:

Q: Suppose y E span{X₁, X₂}. Explain why span{x₁, x2, y} = span{X₁, X₂}.

A:

Q: 2x + 1 3 – 4x Consider the function y = f(x) a) find Ax + h) simplify fully Ax + h) – Ax) h b) find

A:

Q: prove that two vectur ae orthognal A = x + 4y+32 B =4x+2y-42

A: See the attachment

Q: Let A {a, b} and B = {1, 2}. Give an element of A x B x A.

A: Let M and N be two sets. The Cartesian product, M×N is the set of all possible ordered pairs with…

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: Suppose (x1,x2) + (Y1,Y2) is defined to be (x1 + Y2 ,x2 + Y1). With the usual multiplication cx = (…

A: It is given that the addition is defined as x1, x2+y1, y2=x1+y2, x2+y1 and the multiplication is…

Q: v1 =[ 2 5 1 ] , v2 =[ − 3 1 − 1 ] , b =[ 11 19 5 ] Show that b is in Span{v1,v2}. Express b as a…

A:

Q: Consider the algebraic identity (x + y)² = (x − y)² + 4xy By interepreting x, y as line segments,…

A:

Q: a + b+c a + 26 + 4c + 2d` 3. Let m(a, b, c, d) = and set (а+ 2b + 3с + d a+ 2b+ 3c+ 2d) {m(a, b, c,…

A: We have to determine the dimension of the subspace M of M2(R) .

Q: Suppose x,y are real numbers, and 2x+y2 1, then x<1.

A: