6. Show that each of the following are not inner products on R³, (a) (u, v) = U1v₁ + U₂V2; (b) (u, v) = U₁v2U3 + V₁U2V3, for u = (u₁, U2, U3)™ and v = (V₁, V2, V3)T.

Q: assume that Pr[A′]=0.55, Pr[B]=0.35 , and Pr[A′∩B]=0.2. (1) Pr[A∩B]=Pr[A∩B]=   (2)…

A: Solution : Given information; P(A')=0.55 P(A)=1-P(A')=0.45P(B)=0.35 and P(A'∩B)=0.2

Q: 8. Show that (a) i=- (b) j= (c) k= jxk i.jxk kxi i.jxk ixj i.jxk 9. Find the vector triple product…

A: (a)                                (b)                            (c)…

Q: ü = [1,1, 0] and i = [-1,1,0]. Find the cross product

A:

Q: give the general formula of this amount b.) choose those polynomials that contain elements of the

A:

Q: 6. Find UV (dot a) Ū · V = (2, 3, -

A:

Q: Calculate the component of v = 〈− 2, 1/2 , 3〉along w =〈1, 2, 2〉.

A: Given: Vector, v=-2,12,3 Vector, w=1,2,2

Q: For each of the following bilinear forms b : V × V → R, state whether b is product and explain why.…

A:

Q: If A and B are both second-order tensors and t, u, v, and w are all vectors, prove the following…

A: Given that if A and B are both second-order tensors and t, u, v, and w are all vectors.   (1). To…

Q: Show that the points A(8,-1,0), B(0, 1, 1), and C(2, 1, -3) are non-collinear.

A:

Q: 8. Let V={(x,y)x,y € R}. Define addition on V as follows: (x»x)+(x,y)=(x +2x, 1,y+Y,+2) Find the…

A: To find zero vector of V

Q: (5). If A, B and A+B are each non-singular and the products are conformable, prove that (a). A(A +…

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Q: Find solutions of the linear PDE u, + yu, =0 , given that u(0, y)= y'. ди(х, у) ди(х, у) Notation is…

A:

Q: 2. Find vectors v, w E R³ such that v + w = (1,3,7), v is parallel to (1, 0, 1), and w is orthogonal…

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Q: Consider the inner product on R2 defined by ((x, x2), (y, y2)) = x11 + 4x2y2. Which of the following…

A:

Q: Consider the following. u = (-5, 5, 4) v = (0, 1, 6) Find u x v.

A:

Q: d) Let g(x,y) = (3x + y)2(2y + 1) and h(x, y) = 6y2(2x + y) h i) Find дх’ ду’ дх’ ду

A: The given functions are  and

Q: 6. Show that each of the following are not inner products on R³, (a) (u, v) = U₁V₁ + U2V2; (b) (u,…

A:

Q: Show that if v and w lie in the yz-plane, then v × w is a multipleof i.

A: Both vectors v and w lie in the y-z plane, which means they must have zero magnitude component along…

Q: Let a = (3, −4, 9) (a) Find k such that b = (−2, k, −6) is parallel to a. (b) Find k such that b =…

A:

Q: 20. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1,-4,0), v = (-1,–1,2,2),…

A: To find two vectors of norm 1 that are orthogonal to the below vectors.…

Q: Let W (w1, w2, w3) = UxV (cross product) such that U(-3, 3, -3) and V(1, 1, 7) %3D find w2 Answer:

A:

Q: 11) For u = (2,3,-1) and v (-1,01) find; %3D II a) proj,(u) b) The vector component of u orthogonal…

A: For finding projection using the formula, projv(u)=v→.u→v→2v→ The vector component of u orthogonal…

Q: 2. Let A = {2, 3, 5} and B = {x, y}. Let p1 and p2 be the projections of A × B onto the first and…

A: a. Find p1 (2, y) and p1(5, x). What is the range of p1? To find p1​(2,y) and p1​(5,x), we use the…