Let v1 = (1,2,1), v2 = (2,9,0), v3 = (3,3,4) . Show first that S= {v1, v2, v3} is a basis for ℝ^3. Also, let T: ℝ^3 → ℝ^2 be the linear map for which T(v1) = (1,0), T(v2) = (−1,1), T(v3) = (0,1). Then find T(7,13,7)

Q: Find a subset ofbthebvectors v1=(0,2,2,4), v2=(1,0,−1,−3), v3=(2,3,1,1) and v4=(−2,1,3,2)that forms…

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Q: Show whether or not the set of vectors B = {U, V, W} where U = V = and W = 0 is a basis for R³.

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Q: Consider the following maps of polynomials S:P →P and T:P→P defined by S(g(x)) = 4 g (5) – g'(-2)and…

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Q: -3 Let v1 = ----- -2 v2 = 1 v3 = -6 3 -3 v3}. Find the basis for H. and the H = span{v1, v2,

A: we are given three vectors  v1=-3-2-3,v2=-21-2,v3=1-63 we have to find the basis for H.

Q: Find the bilinear transformation which maps the points (-1,0,1) into points (0,i,3i)

A: the bilinear transformation which maps the points (-1,0,1) into points (0,i,3i)

Q: Q3. a) Express the vector (4,2) e R' as linear combination of the vectors (1,1) and (1,-1). b) Let T…

A: We have to find all these

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Q: d. Find the transition matrix from C to B. e. Find the coordinates of u = (2, –2) in the ordered…

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Q: Suppose T: R¹→P3 is a linear transformation whose action on a basis for R4 is as follows: -3 0 ਏਕ ਦੇ…

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Q: Find the coordinate vector of a = [*]B= -10-30- 2 with respect to the basis B = for R³.

A: Given: It is given that, x→=42-4 and B=152, 01-6, 001. To find: We have to find the coordinate…

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: (1 point) The matrices - [8]. [J]. -[i]·.^ - [i]· A A4 = A₁ = A3 = A₂ = form a basis for the linear…

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Q: Show that u1 =(2,1,1) u2= (-2,2,1) u3= (1,-1,-2) are linearly dependent show all working and explain…

A: Given :u1 =(2,1,1) u2= (-2,2,1) u3= (1,-1,-2)

Q: Calculate 121x dxdy where R is the parallelogram with vertices (0,0), (6,2), (7,6) R 1 -(v — Зи), у…

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Q: 10. Let (1,2,3) be a solution for the vector equation ru + yv + zw = 0 and consider the matrix…

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