B.4 Find the orthogonal projection of the vector (1,2..n) on the orthogonal complement M- of M in E M = {u € E : 2r1 + r3 - 4 = 0, r1+3r2 + 2r3 +x4 = 0}

Q: would the two vectors be (1 1 1 0) and then (0 0 0 1)?

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Q: Consider the following. u = -7i - 4j - 2k, v = 4j + 4k (a) Find the projection of u onto v. -12 2k X…

A: Given :u=-7i-4j-2kv=4j+4k

Q: Find the vector projection of b = 6î + 3ĵ + 2k onto å = î – 2ĵ – 2k.

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Q: 1) The domain of the vector position r(t) = 1+2 i+ sintj+ In(9- t²) k

A: We are entitled to solve only 1 question at a time so, I am providing you the solution of the first…

Q: find all values of the scalar k for which th e two vectors are orthogonal.

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Q: B = {1+t²,t +t?, 1+2t +t²} is a basis for P2. Find the coordinate vector of p(t) = 1 + 4t +7t²…

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Q: 8) Find the unit tangenit vector TilE) at the poin Let ř(t)= <-5t'+3, Be -S sin (E)) 3t -3t -5cos…

A: Given curve r→t=&lt;-5t5+3,3e-3t,-5sint&gt; We need to find tangent vector T→t at t=0. Tangent…

Q: 2. Find the value of a for which the vector à = (axy – z³)î + (a – 2)x²j + (1 – a)xz²k have it's…

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Q: For what values of the scalar t are the three row vectors (t,3,0), (3,t,3) and (0,3,t) linearly…

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Q: +5 c) Let y = n44| and u = is Span{u} and one orthogonal to u. where n=9. "t. Write y as sum of two…

A: y=nn+4 and u=n+5n-1. We have to write y as the sum of two orthogonal vectors, one is span{u} and one…

Q: -91 Let y = -3 and u = and 2 orthogonal to u. x₁ = 4 -2 Write y as the sum of two orthogonal…

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Q: 5. (S.15). Let ит —D (-1,1,3), из — (2, 1, —3), из Find expansion of the vector v= (-3, 2, 4) via…

A: By using simple linear algebra we find expansion of v via vector u1 , u2 , u3

Q: c for which the following vectors vi = %3D 1 P4 = are linearly independent. 1

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Q: Assume that 0 < a <1 and 0 < b <1.Find the stable vector of 1- a a P = b 1-b w = [ ]

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Q: Find the Wronskian of the following vector functions: 3t-1 -t+1 u (t) = -t v (t) = 3t

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Q: 3- The scalar component of the vector F in the direction of K is (K.F А- .K, В- K C-

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Q: 2. Find the magnitude of the vector PQ whose initial point is P(1, 2) and end point is at Q(4, 3).

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Q: Consider the following. u = -8i – 4j - 2k, v = 4j + 4k (a) Find the projection of u onto v. -3j – 3k…

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Q: Determine the residual and Jacc - bian needed to solve the equation d²u 2u° = 0, - dx? 1 and u(1) 0,…

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Q: Given the operator S on the vector space R₁ [x] given by S (a+bx) = -a+b+ (at 2b) x A) What is SC1)…

A: We know that Pn is the vector space of all the polynomials of degree n+1 and the basis for this…

Q: 3 (c) Let ¤ = Find the vector in col(A) which is closest to T. 2

A: Consider the matrix  A=[1-1414-21421-10]We first see whether the colums of A are linearly…

Q: Suppose T(v1) = w1 + w2 + W3 and T(v2) = w2 + w3 and T(v3) = W3. Find the matrix A for Tusing these…

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Q: Find all values of the scalar k for which th e two vectors are orthogonal.

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Q: Is v = |1a vector in the span of S = }|2| Use Gaussian elimination to support your answer.

A: To check v=111 a vector in a span of S=123, 012, -201 or not.

Q: The set B = {1 – t2, t – t², 2 – t + t²} is a basis for P2. Find the coordinate vector of p(t) = 1+…

A: The coordinate vector of p(t) relative to B will be [p(t)]B

Q: 1. Consider the vectors a = (1, 1, 1) and y = (1, 1, 3) in Rº. Compute æ x y. 2. Show that, for æ, y…

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Q: 1 Find the vector projection of u onto v. u= 3i- 5j ++ 2k v=7i+j- 2k

A: Please refer the attached image for complete solution.

Q: Let u1,...Ūk E V be linearly dependent vectors, and k > 2. Prove that there exists j, 1 < j < k,…

A: Given- Let v1→, ……, vk→ ∈ V be linearly dependent vectors, and k ≥ 2.  To Prove- Prove that there…

Q: Find the equation of the plane E passing through the point P(2,3,1) and parallel to the vectors K =…

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Q: 4 If r(t) =(1+t)3/2i+(1 - t)/2j + tk, t= 0 then the binormal vector B is

A: Consider the position vector,   rt=491+t32i+491-t32j+13tk,   t=0                      Orrt=491+t32,…

Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: Given, Normal,n=(2,-4,1) Point, P=13,23,1     Find the equation of the plane with normal vector n…

Q: X/ Find The normal vector to A = 2i-3j+4K , B = i-2 j+ 5K AxB=Ñ =? ĀXB=N -3 4 = -7i-6j-K %3D - 2 Hw/…

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Q: 5. Let T: R2 R be defined by [x1 +2x2 T a. Find the matrix [T]B.B relative to the bases B = {u,, u}…

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Q: "If u E R' is a nonzero vector, then there exists a vector v E R° so that the matrix A = (u v) has…

A: Given statement is true.

Q: 1. Determine if the vectors e2t and e-t are linearly inde- e2t e-t pendent/dependent.

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Q: d) Find the orthogonal projection of v = 1 into U+. (1)

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Q: If r(t) = (1 + t)/²i+ (1- t)/2j+tk, t 0 then the binormal vector B is اخترأحد الخيارات

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Q: Suppose T: R³ → R² is a linear map and that u and v are particular vectors in R. If T(u) = (2, –3)…

A: Given query is to find the indicated vector.

Q: Find a nonzero vector u with initial point P(-1, 3, -5) such that u has the same direction as v =…

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Q: 11. For what values of c are the vectors [-10 -1, 12 1 2], and (1 1 cl in Ra linearly dependent? 12.…

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Q: 10. Let the vector v = 2i -3j + k, and the vector w = = -i+3j+ 2k. Find v x w.

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Q: Find the Wronskian of the following vector functions: 31 e -31 e 3t v, (t) = -3: v2 (t) = -3 e -3:…

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Q: Consider the vector-valued function F(2,) = [xy² + 2ye* х, у y 3xe-y Which of the following are NOT…

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Q: (c) (d) spaces What is the matrix of T with respect to the standard basis of both vector What is T(2…

A: As per the question we are given the matrix form of a dual transform T* and we have to find the…

Q: Find the Wronskian of the following vector functions: 4: -21 41 4t v, (1) - 2 (1) - -4 e 21 ", (1) =…

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Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector of 1 - a а P = 1 - b [ W =

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Q: Find the standard matrix A and A' for T = T2 • T1 and T' = T, ° T2, where T1:R2 → R³,…

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Q: 1 Find the domain of the vector function r(f) = 4ti+ %3D t-2J O (0, 4)U(4, ) O (o, 2)U(2, ) O…

A: The domain of vector function is all values of t for which its each component function is defined…

Q: S. The image of the vector i + j – 2k under a mapping (1 2 3 defined by the matrix M, where M = 0 1…

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Q: 2. Let u e R™ and v E R be two non-zero vectors, in other words at least one component of the…

A: Given: Let us consider the u∈ℝm and v∈Rn are two non-zero vectors and assume A=uvT∈ℝm×n. a) Presume…