4. Let T: R4 → R³ with T 0-1 = a. What is the domain of T'? C. b. What is the codomain of T'? x + 2y + z -3x - 2y + 3w 4y + 3z + 3w 1 H 5 2 What is the image of under T'? 2 d. Find all the vectors that T maps to -1 H 5 Is T one-to-one? Justify your answer. f. Is Tonto? Justify your answer. g. Describe the kernel of T. Give a basis for it. h. Describe the range of T. Give a basis for it.

Q: 4- Determine whether the vectors v1 = (1, –1, 2), v2 = (3, 2, – 1) and v3 = (5,0, 3) form a linearly…

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Q: Determine the vector fald of . Fa, -- %23

A: The given vector field is                                            V(x,y)=4i-2j

Q: The dot product of two vectors can be written in the form x = 00 s+ X1 X2 and y = in R" is defined…

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Q: (-2,3,1,0,2). Find scalars a and b so that аи + bv 3 Let u = (2,1,0,1, –1) and v = (-8,8, 3, – 1,7).

A: u=2, 1, 0, 1, -1  &  v=-2, 3, 1, 0, 2

Q: 1. Consider the pointsS= (1,−3) andT= (2,5).(a) Sketch the vector−→ST.(b) Give the component form…

A: Here 2 different problems are provided. As per our Bartleby Guidelines, we are supposed to…

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: 1. Compute the following for the vectors in R3, x [1 3 21T and y [40 1T y and y x (a) (b) 2 and y2…

A: From the given information, [1 3 –2]T and [4 0 –1]T.

Q: Consider the 4-vectors Aª = (a, 0, 2a, 0) and Bª = (23, 0, 0, 0), where a and 3 are non-zero real…

A: and .It is given that  is null vector.

Q: Let j = | and ü .Write j as the sum of two orthogonal vectors, it -2. %3D an {u} and ¤2 orthogonal…

A: Given:- →y=-69  →u=5-2

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: -3 3 Let u = -5 and i: 7 Find a vector w not in span {u, v}. 4 -3

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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: Find any two non collinear vectors on the plane x-y-3z +6=0

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Q: Consider the following function. T: R² R³, T(x, y) = (√x, 3xy, √y) Find the following images for…

A: Let us consider the transformation T:U→V defined as T(u)=v  The transformation is linear…

Q: Let y = #₁ = 1 and = 2 -27 -2 Write y as the sum of two orthogonal vectors, 1 in Span{u} and 2…

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Q: Q1. If O (0,0,0) in (x,y,z) 3-D space and r(2,5,1) draw the vector in 3D and find its direction.

A: Plot point in 3D

Q: 2. (а) ở and w are vectors in R? such that f(0) = w. Express f(27 – 3w) as a linear combination of i…

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Q: 5. Determine whether or not the following vectors i R³ are linearly dependent: (1, –2, 1), (2, 1,…

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Q: Suppose u, v and w are non-zero vectors in R" such that proj(-2v) a and proj(5w)= b. Use the…

A: Projection vector of a→ in the direction of b→ Proj b→a→= a→.b→b→×b^=a→.b→b→b→2

Q: Find the Wronskian of the following vector functions: u(t)= 5t-4 -t · -| V v (t) = -t+4 5t

A: Let  ϕ1(t)  and ϕ2(t)  are two vector valued function  Wronskian of these  vector functions is…

Q: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

Q: Consider the vectors u₁ = and the vector w = 3 H Q- W U2 = []} Uz = U2+ →→→→ →→→→ If u IS in the…

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Q: Q10. 4 A is a condtant vector and R= 3xí + 3yj +3zk, then grad ( 3A.-R) = ? (a)A (6)3A (C) JA /d)…

A: Let us have the constant vector A=ai^+bj^+ck^ Here, a,b,c are fixed real numbers. Now,…

Q: -0-0--0--0--0- 1 19. Let S be a set of vectors such that u = whether the set of vectors is linearly…

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Q: Q1. Construct an orthogonal set of vectors from the following vectors: X1 = k,X2 ,X3 %3D 14]

A: Use the usual inner product in the vectors and Gramm-smidth orthogonalisation process.

Q: 2 Let I be the line in R³ that consists of all scalar multiples of the vector w = -[] 2 Find the…

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