Q) show that the pánts ACI,1,4), B(2,2,2), C (o,1,5) and D(1,0,5) ave coplanear (in the Same plane).

Q: Find one voctor in R' that spans the intersoction of U and W where U is the xy-plane-that is, U =…

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Q: Find inner product of u, v and || u || if u = (1,2,5) and v = (2, –3,5). (Ctrl) -

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Q: Show that except in degen-erate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w)…

A: Show that except in degenerate cases, (u x v) x w lies in the plane of u and v, whereas u x (v x w)…

Q: Consider the collection of vectors --000 1 Is Slinearly independent? Carefully explain your answer.

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Q: Select the orthogonal projection of (1,1,1) onto the span of (1,0,1) and (1,1, – 1) in R. O (2, 1,…

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Q: a. Show that Ø, R E T. (by definition of Topology)

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Q: 2. Find the volume of the parallelepiped having a = (1,4,–7), b = (2,–1,4) and c = (0,-9,18) as…

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Q: - Show that the norm tion t= aT+B. Use [a, b] onto [0, 1] (7) = 1, ý(7)= T, V т,

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Q: (2,3) is te i చాంబ! Under a ro dediona Identidy three distinct point that Cald be the center & of

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Q: 32. In APQR, mZP = 53°, PQ = 16, and QR = 10. Find m2Q. %3D %3D %3D 32. In AJKL, mZL = 113°, JK =…

A: 32. Here, we have given the length of two sides and measure of one angle of △PQR. So we will use the…

Q: Let U(9, 9, 2), V(9, t, 4), and W(2, 5, 8). U, V and W have the same starting point. find t for…

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Q: 12. Find the volume of the parallelepiped spanned by the vectors (1, 1, 2), (2,2, 1), and (0, –4,…

A: The given vectors 1,1,2, 2,2,1, 0,-4,0

Q: Find the Theishts ave defined by ECX,y) and bases are the regions bounded by the fallawng fontion in…

A: Given: Height of solid is defined by zx,y=16-x2-y2, R:    y=2x    and     y=4x-2 To find: Volume…

Q: Find the set of ordered pairs (T0, Yo) for which Picard's Theorem guarantees that the IVP y ry %3D y…

A: Given,            y'=xyx+y, y(x0)=y0

Q: we divesgencatheosem to evaluate + XzK. dA cohose sisthe boundasy of cube definedd by

A: By divergence theorem we convert the given surface integral to the volume integral, and the region…

Q: (a) Find the length of the projection of w onto v given that w = (4,7) and v = (1,1).

A: Given: w=4i+7j, v=i+j we know that projectionp→ of w onto v is given by p→=w.→v→v→2v→

Q: Which of the following vectors is coplanar to [1, 1, 1] and 2, 3]?

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Q: Let Z, = 2 cis 30° = 3elli %3D Z = In (1 + i) %3D If Z = Z,Z, + Z, Find Z].

A: From the given information. Write the complex numbers Z1, Z2 and Z3.

Q: Find a non zero unit vecor î that is orthogonal to u1= (1,2,1) and Uz= (2,5,4) in R³.

A: The given vectors are u1=(1,2,1) and u2=(2,5,4) in R3

Q: Let T cofinite topology on R and Y={5,6,7} find Ty?

A: We have to construct subspace topology with respect to the cofinite topology

Q: Find the projection of u onto v if, u= (4, 2), v = (5, -2).

A: Given, Formula for the projection of u onto v is given by

Q: Let = (0,- 2)v=(3,2) and w=(-2,1) Then the dot product u. (V w) is equal to

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Q: For what values of m and n are vectors [m,n,1], [2,1,3] and [2,1,1] coplanar?

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Q: 5) Suppose that the set of vectors {ỉ, 7, w} is linearly independent. Prove that Span({ū, T}) #…

A: Given that u→,v→,w→ is linearly independent. Prove Spanu→,v→≠Spanu→,v→,w→.

Q: show that the pants AC1,1,4), B(2,2,2), c(o,l,5) and D(1,0,5) coplanear (in the are Same plane).

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: (K", || |,) is called the LP-norm on K". is a normed linear space for 1 <PS00. || |,

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Q: The vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain,…

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Q: Show that close ball Y in a metfic space (X,d) is a closed set also show that if (X,d) is complete…

A: Show that closed ball Y in a metric space (X,d) is a closed set also show that if (X,d) is complete…

Q: Find the moment vector m and m of p = [2,3,0] about Q: (2, 1, 0) acting on a line through A: (0, 3,…

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Q: Find a vector a with representation given by the directed line segment AB, where A(−5, 0, 1) and…

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Q: Show that there are infinitely many vectors in Rwith Euclidean norm 1 whose Euclidean inner product…

A: For a vector (a,b,c) its euclidean norm is given by a2+b2+c2. Euclidean inner product of two vectors…

Q: Define the det product ICl=C_ d s à and B, which ane glven as A=An T'+ Ay+ Az and B Bx?+ By BzP in…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: compute the component of u along v. u = (3, 0, 9), v = (1, 2, 2)

A: the given vectors are: u=3,0,9v=1,2,2 we have to compute the component of u along v.

Q: 3. If x and y are two n-vectors, then prove that 1 (a) |x*y|< ]], \»l, - +=1 (Holder inequality) 1…

A: Given that x and y are two n-vectors. We have to prove the following :                          (a)…

Q: Prove that if A is skew-symmetric matrir, Q = et is orthogonal.

A: c) To prove:- If A is skew-symmetric matrix , Q=eAt is orthogonal. Proof:- Ais skew-symmetric matrix…

Q: If ã = <!,2,37 and b=<5,0 -17, find the vector pojection of %3D %3D ŏ onto à.

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Q: If x, y are two no vectors, then prove that |xty | || X lle y llq by = + // use Holder inequality.

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Q: Find the projection of u onto v if u= (5,-3), v = (-1,4).

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Q: д(х, у) Find the Jacobian of the Ə(u, v)

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Q: 19 - By using the definition of the dot product, which vector is orthogonal (perpendicular) to å =…

A: Dot product of two vectors

Q: The vector norm is always positive.(i.e. ||X||>0 for every vector X.) Select one: O True False

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Q: Compute ∮c (ydx+zdy+xdz) where C is the triangle with vertices (3,0,0), (0,0,2), and (0,6,0)…

A: The given points can be plotted as A(3,0,0) B(0,0,2) C(0,6,0)

Q: 2. Let W = Span {u1, u2, uz3, U4, U5, U6}, where 4 1 , U5 = Uj = U2 = u3 = ,u4 = U6 = 2 2. 4 What is…

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Q: Show that there are infinitely many vectors in R^3 with Euclidean inner product with (1,-2,4)is zero

A: Given vector is (1,-2,4) in R^3

Q: 2. Show using only the Cauchy-Schwarz inequality that if u,vE R", then || u- v ISl u || +| v | (1

A: Solution

Q: Find three numbers a1, a2, az to normalize the orthogonal set 1 in R³. aj = a2 = az =

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Q: 1. Compute the angle Pair Of vectors in Standard inner producy on Mzz. between tre following Mzz…

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Q: Let X = (!,2) and T3} U = (1,2-)inel,2,U+ jult. %3D n+1 show that X is not T - space

A: This is a problem of Topology.

Q: Compute / (1/zy, 1/(z + y)) dr along the path from (1, 1) to (3, 1) to (3, 6) using straight line…

A: The parametric vector form of a straight line from (1,1) to (3,1) will be given by:…