If i and i are in R™, then –i is in span {ū, 3}. |

Q: 1. Let U2 = 2. fui, 4.} is an orthonmal basa fo IR Show that

A: The set of vectors v1,v2,…,vn of a vector space V are said to be an orthonormal set of vectors if…

Q: prove thats. u.w V.W V.

A:

Q: 8.0. If x-(x,, X, ...,%)«R', define [xL by Prove that xJkL is a norm on R'. N I|} dns - x]

A: We will solve the first question highlighted in yellow. If you want the second question to be…

Q: Let u= and v= Show that is in Span (u, v} for all x and y.

A: Given u=4-1 , v=41 and b=xy. The vector b=xy is in span u,v if the system containing u,v and b is…

Q: Suppose v1, V2,..., Vm E V. Prove that {v1, v2, ..., Um} = (span(v1, v2, ..., Um))-.

A:

Q: Prove that the four points P(2, ;1, 1), Q(1, 3, ; 2), R((2, 1, ; 3) and S(3, 2, 0) are coplanar

A: Given four points are  P(2,1,1)Q(1,3,2)R(2,1,3)S(3,2,0)

Q: prove that 2. catX+c

A: We use that- sin2x + cos2x =1  so that 1-cos2x= sin2x

Q: Compute the dimension of Span (v1, V2, V3, V4, V5, V6 ).

A: Follow the procedure given below.

Q: Consider the following. u 3 (-4, =(-4, 6), v = (1, 1) (a) Calculate projy u.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

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 these statements best describes the trlangle?

A: Law of sine: - The rule of sines is the ratio of side length to the sine of the opposing angle in…

Q: Find the projection of u = onto v = . projuv =

A: We can find the projection in two form one is in scalar form and other is vector form. here i give…

Q: 3 Compute the projection of i on ū = 1 proj, v =

A: The given vectors,v→=30-3  ,  u→=31-1

Q: What is u × w, assuming that w × u = 〈2, 2, 1〉?

A: Given,w×u=2,2,1 To find:u×w Solution: We know ,by property of cross product of two vectors (say,a…

Q: 2.44 Show that if a vector is in the span of a set then adding that vector to the set won't make the…

A: The given statement is " if a vector is in the spanning set then adding that vector to the set would…

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: {[: :}[: }} 1 2 1 0 1 -1 1

A:

Q: Let u = and v = Show that is in Span (u, v} for all x and y. y -1 5

A:

Q: Show that w is in span(B).

A: Given that: B=120,120, w=1188 To show that w is in span(B).

Q: Find the norm of the projection of u onto a ( || proj,u || ) with the following: (a) u=(1, – 2). a…

A:

Q: Find r, s, and t so that (a) z = 1 2 x, (b) z + u = x, (c) z − x = y.

A: Given  And z+u=x and z-x=y. We need to find the value of r , s and t.

Q: Find (a) projvu and (b) projuv. Use the Euclidean inner product.u = (1, 2, −1), v = (−1, 2, −1)

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Q: Theorem: Proper ies of Transposes 3.) %3D

A: If we take transpose of transpose matrix, the matrix obtained is equal to the original matrix.…

Q: Prove that u + v and u - v are orthogonal in Rn if and only if llull = llvll.

A:

Q: Let {V1,V2,V3} be a set of vextors in Rn. If u is in Span{V1,V2,V3} , show that 3u is in…

A:

Q: Let W = Lin and U= Lin 2 (a) Show that R' = W U. Explain.

A: Note:- As per our guidelines, we can answer the first part of this problem as all the parts are…

Q: Find (a) projvu and (b) projuv. Use the Euclidean inner product.u = (−1, 4, −2, 3), v = (2, −1, 2,…

A: Given:

Q: LBe M, N subsets of space W. Then span (MUN) = span (M) + span (N)“ %3D

A:

Q: Show that R³ is spanned by S = {(1,1,1), (1, –1, 0), (0, 1, – 1)}.

A:

Q: The set S=[1,3) is not compact. Which open cover of S contains a finite subcover?

A: This is the question of Topology.

Q: 7. If in an inner product space, (x, u) =(x, v) for all x, show that u = v.

A:

Q: Find and when (TU – V)² In(W – UV) = In(2) at the point (T, U, V, W) = (1, 1, 2, 4).

A:

Q: Let a = (- 4, 3, – 2) and b = (- 1, 2, – 3). Find the projection of b onto ä. proją b > V

A: Answer:Given a→=<-4,3,-2>b→=<-1,2,-3>projection b→ onto a→ is given…

Q: . Prove that u, v, and ware all in span(u, u + v, u + v+w)

A: Given: Prove that u, v, and were all in span (u, u + v, u + v + w)

Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y4…

A:

Q: Supbose A, B and c in vestible matnices , show also invertible AB C is that by baioducing matnix D…

A: Let A-1, B-1 and C-1 denotes the inverses of matrices A, B and C, respectively.Show that ABC is…

Q: Let A be an wmxn matcix Prove that %3D

A:

Q: Let V, 3 V3 = Vz= -3 8. %3D 131 2- -5 does { Vi,UeiVa} span R3?

A: Given vectors, v1 = 06-2 , v2 = 0-38 and v3 = 4-1-5 These vectors will span ℝ3 if they are linearly…

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: If u and v are orthogonal, show that projv u = 0.

A: If u and v are orthogonal, show that projv u = 0

Q: The Canonical form of a hyperbolic PDE is F (ξ, η , u, ug , un ) %3D False True

A: To check the given statement is true or false. Given that the canonical form of a hyperbolic PDE is…

Q: Prove that u, v, and w are all in span(u, u + v, u + v + w).

A: To Determine: prove that u ,v and w are all in span (u,u+v,u+v+w). Given:  we have(u,u+v,u+v+w)…

Q: Find the projection ofv onto u

A: We  have to use the projection formula according to the projection here we have on two vectors. we…

Q: Let ā = (4, – 1) and b = (– 2,0). Find the projection of 5 onto ā. proj, 5 %3D

A: Let a→=4,-1 and b→=-2,0 To find projection of b→ on a→

Q: Find the pnjection of the verter v ento the Subipand S. S= span V= projs V=

A: From the given information. The subspace S and vector v are as follows. S=span01-10,0-1-1-1v=1110

Q: Prove that Srxdr = 2[, , da, r × dr =

A:

Q: Let à = (1, − 1, — 5) and 6 = ( – 5,0,− 1). Find the projection of b onto a. proj¡ b = >

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Q: Suppose that A = SS−1, where  is a diagonalmatrix with diagonal elements λ1, λ2, . . . , λn. Show…

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Q: Let ä = (4, – 4, 0) and b = (- 1, 2, - 4). Find the projection of b onto a. proj, b = <

A: