Find all possible real numbers a, b, c, d E R such that form a basis B= (v.w) for R² that satisfies v- (a) and w- () w= [()L-() Warning: Do not forget to check that your possible choices of a, b, c, d ensure that v and w are in fact a basis for R².

Q: Determine whether the vectors (3,0, 3, 6), (6,0, 0, 3), (0,0,3,0),(6,3,9,12) form a basis of R*.

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Q: Find the coordinates of the vector (2, -3, 4, -5) relative to the basis (0, 1, 0, -1), (1, 0, -1,…

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Q: Which of the following cannot be defined as an inner product between two vectors (x0, Yo) and (¤1,…

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Q: With T defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is…

A: The given matrix  and the vector  and  is defined by .The aim is to find the vector  whose image…

Q: Use the function to find the image of v and the preimage of w. T(Vy. V2) = ( V2, 2v1 - v2), v = (7,…

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Q: (a) Show that the vectors v1 = (1, 2, 3, 4), v2 = (0, 1, 0, – 1), and v3 = (1, 3, 3, 3), form a…

A: (a) The given vectors are: v1=(1,2,3,4), v2=(0,1,0,-1), v3=(1,3,3,3)

Q: Let the following vectors be in R³ a = (1,3,-1) b= (-2,1,3) c = (3,2,1) d = (1,-1,2) 15.- Find the…

A: Introduction: Vector Operations are operations that are performed on vector quantities. Vector…

Q: V2, V1 + v2, 2v1 - v2 ), v = (9, 9), w = (-3/2, 2, -8) (a) the image of v (b) the preimage of w (If…

A: This is a problem of vector calculus.

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 - V1, Vị + V2,…

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Q: 4 r 1 by -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A: First we find p, q, r and s. Then solve it.

Q: Find the coordinate vector of = 48 [B = 5 -1 with respect to the basis B = 0 {} for R³.

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Q: If B is the standard basis of the space P3 of polynomials, then let B = {1, t, t², 13³). Use…

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Q: Determine whether B={1-31²,2+t-5t².1+2t) is a basis for P2.

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Q: 7. Let +-() वे = -2 and -4 2 3 Find a real number x and a vector such that = -x and 17.

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Q: b) Let v1 = (1,2,1), V2 = (2,9,0) and vV3 = (3,3,4). Show that S = (V1, V2, V3) is a basis for R³.…

A: Explained below...

Q: Find non-zero vectors I and 7 that are both orthogonal to and orthogonal to each other.

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Q: Use the function to find the image of v and the preimage of w. T(V₁, V2, V3) = (4V2 V₁, 4v₁ + 5v₂),…

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Q: The velocity vector of a particle in the xy-plane is (√7, 9e³-3) for all real t. If the position of…

A: The velocity vector in the xy-plane is for all real t. If the position of theparticle at , then to…

Q: Prove that a(-3,2) and b (2,-3) form basis vectors in xy plane

A: a set is said to be basis if set is linearly independent and it spans the space.

Q: Represent the vector ⟨16,8,−14⟩ in terms of the ordered basis B={⟨5,−2,−2⟩,⟨1,−4,2⟩,⟨−1,−5,3⟩}.

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (v2 V1, V1 + V2,…

A: Let us consider the transformation T: V→W defined as T(v)=w where v is preimage of w  and w is an…

Q: Determine whether the set of vectors Q={(-1,1,1).(-1,0,2).(1,2,3)} spans R'.

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Q: 44. (a) Find all vectors v such that (1.2.1) X = (3.L-5) (b) Explain why there is no yector v such…

A: To find vectors v?

Q: = (2,1,0,3), v2 (0,1,5,7), v3 = (0,0,3, –1), v4 = (0,0,0, –4) b) V1

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Q: Use the function to find the image of v and the preimage of w. T(V,, V2, V3) = (4V2 - V,, 4v, +…

A: To find the image of v , we have to pass v to the input of T.   To find the pre-image of w, we have…