Let V =(1,2,3,4),V=(0,2,t,3) and w=(!,!,,1) 1. Find t so that u t v and w are to each other. or thogonal

Q: a u, (00) = Utt , и (0, t) — 0, и (т, t) — 0, (t>0) и (х, 0) %3D0, (0<x<n, и, (х, 0) %3 * (т—г),…

A: We need to find the solution to the threshold problem in the next wave equation by the variable…

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Q: Evaluate | Vtan a sec" zdx. O a. 2 z tani z +tani +C 2 O b. 2 tani æ + tan +C 2 Ос. 2 O c. 2 2 t…

A: To evaluate the integral,  ∫tanxsec4xdx Rewrite the term sec4x=sec2x·sec2x…

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: If u = (0, 2, 3) and v = (1, 3, -1), find the projection of u onto v. 이름다 a) Obl 이유ㅎ ○ c) (1, 1, -1)…

A: This question can be solved using the concept of vector projection of a vector on other vector.

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: 1. Show that S, has the presentation (x, y|x² = y = (xy)² = 1). %3D

A: The symmetric group S3 is given as S3=I, 1 2, 1 3, 2 3, 1 2 3 1 3 2 where  I=123123, 1 2=123213, 1…

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A: Given, U2=I

Q: nts A and B have symmetry with respect to the ) (9, 2) (х, у) %3D -) (0, 8) (x, y) =

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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Q: Prove that u, v, w ∈ R3     and [ u x v, v x w, w x u] = [ u, v, w]2

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Q: Let u = (2,3, 1), v = (1,3,0), and w = (2,23, 3). Since (1\2)u – (2\3)v – (1\6)w = (0,0,0), can we…

A: No we can't

Q: XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1).  Which of the following can be used to prove that…

A: The answer is given as follows :

Q: Prove (t, to) = A(t)Þ(t, t,)

A: The variables of function t and to are independent variables.

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: 1. Let u= (0, -2,3), v= (1,4, 1). Evaluate a) the projection proju(v) of v over u And b) the area of…

A: Given: Let u= (0,-2,3)   and  v=(1,4,1) To find a) the proju(v)  of u over v b) area of the…

Q: Let X; ~ X"(1) i= 1,2, . - ·, n and assume they all uidependent are Y = Ź Xi %3D しニ」 ان منتتفينتمنل…

A: Given, Xi~χ12 ,i=1,2,...,n a. Y=∑Xii=1n Therefore, X1+X2+.....+Xn~χn2 above is possible using…

Q: ag show that: coth's =ţ he (xal/, X-1

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Q: Prove Theorem (rA)T = rAT

A: Consider the matrix A=a11a12a13...a1na21a22a23...a2na31a32a33...a3n...............am1am2am3...amn…

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

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Q: Show using MGF technique that if Z, - N(0,1), for i = 1,2,3,4,5 , then U = Ez - x² with 5 degrees of…

A: Using the MGF technique we have to prove that : U = ∑i=15Z2i ~ χ2 with 5 degrees of freedom, If Zi ~…

Q: Prove that • I %3D

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Q: Let ā = (- 4, - 5) and b (- 5, 0). Find the projection of b onto ä. Round your answer to at least 3…

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Q: Let v1 = (1,1,2) v2= (-1, 2, -2) v3= (-2,-1,1). Write u = (6,7,2) as a linear combination of v1 v2…

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Q: Let S,(x) = 2x³ – 3x² + 3x – 4, 0<x < 1, S,(x) = x³ + b,x² + c,x + d,1 sxs 2. Find b,, C1, d, that…

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Q: FIR R whose by (1,213) qnd (4,5,6) a) Find Iinear mapping Image is generated

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Suppose that u = (0, 1,-2) and v = (1, 0, 1). Compute the projection of u onto v. Enter the…

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Q: ) Prove that sac"()/T sec

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Q: b) Verify uxy = Uyx , if u = In /x² + y² . %3D %3D

A: Consider the given function. u=lnx2+y2 To verify the equation, find the derivative first with…

Q: 2- Find x, y, z, u, t, v such that 2 3 8. 3 5 +2 9 8 14 a) X =-6, y = -1,Z = -1, u = 1,t=2,v= 2 %3D…

A: xyzutv+2123456=8359814   To find : the value of x, y, z, u, t

Q: 2 Given u -1 and U , for which w is the set {u, v, w} linearly independent?

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Q: Let F(x, y, 2) = (z, 1, y). a. Find divF and curlF.

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Q: Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=Ỹ.

A: Given  that  y→1, y→2, y→3∈ℝ5 and that                   y→1+ y→2+ y→3=0→. and           Y^=spany→1,…

Q: Suppose vi, v2, ..., m is linearly independent in V and w ɛ V. Show that v1, vz, ..., Um, W is…

A: v1, v2,......., vm is linearly independent in V and w∈V

Q: If w = f(u, v), u = x + y, and v = x - y, show that w,wy = w - w?. %3D %3D

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Q: If x = v'u and y = 2uv, show that JJ' - 1, where J is the jacobian of u,v with respect to x and y…

A: We have find the jacobian

Q: et §, ŋ, o be real numbers and consider ctors (1,5,§³); (1,ŋ,n³); (1,0,0²). Determine e conditions…

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Q: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w. Provide example

A: Consider that x is orthogonal to v and w To check is it true that x is also orthogonal to v − w.   a…

Q: Question #30

A: Note: Some of the basic calculations are directly written due to the question being very lengthy. We…

Q: Prove that u, v, w ∈ R3     and [ u x v, v x w, w x u] = [ u, v, w]2

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Q: Prove that ||ū – w||< ||0|| + ||w|| where ū = (i, –2, 1+i) and ū = (1,2+i, –i).

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Q: Find w such that 2u + v u 3w = 0. (0, 2, 7, 5), v = (-8, 4, -3, 1) 1 -- (-) W = 3 -

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Q: The function u, takes on the following values : 1 1 1 1 1 u, = , u. + .....u, 10 1 + 3+1 + 32 +…

A: SOLUTION-

Q: If G (x, y, z) = curlF (x, y, z), where F (x, y, z) = (y – 2, z – x, x – y), then х, х — у), then ||…

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Q: Find (u, v), ||u|, |v |, and d(u, v) for the given inner product defined on R". u = (-5, 4), v = (0,…

A: We have given vectors u and v,  And we have to find a), b), c) , d)

Q: Find (u, v), ||u||, ||v||, and d(u, v) for the given inner product defined on R". u = (-5, –12), v=…

A: For the given inner product

Q: Suppose {u,..., 4,, W1, ..., W,} is a linearly independent subset of V. Show that span (u;)…

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

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

A: