Consider the Euclidean inner product space R³ 3 with basis B={(1,1,1),(0,1,1),(0,0,1)}. a Find an orthogonal basis of R³. A. {(1,1,1),(0, 0, 1), (0, -1, 1)} B. {(1,1,1),(-2, 1, 1), (0, -1,1)} C. None in the given list. D. {(1, -2,1),(0,-1,-1), (0, 1,0) } E. {(-2,1,1), (0, 1, 1), (0, -1,1)}

Q: The set B = {1-1², 2t-12², 1-1-1²) is a basis for P2. Find the coordinate vector of p(t) = 3 +…

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Q: 1. Say whether the following vectors are linearly independent and whether the vectors form a basis…

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Q: 3. The set B = {1-t², t-t²,2-2t + t²} is a basis for P2. Find the coordinate vector of p(t) =…

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Q: In Rª, let S = {(1,2,2, –1), (0, –1,4, 2)} and T = U = sp(S) and W = sp(T). Find a basis for U +W…

A: Your approach is absolutely right!

Q: Let B = O If the coordinate representation of the vector in the basis B is representation of 7 in…

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Q: 3 ={0.2) 14 The vectors B = 1 (2³) B = [ ²5 ] form a basis. Find a vector x given the B-coordinates…

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

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Q: Consider the basis D = {(1, 1, -1), (2, 1, 3), (-1, 2, 1)} of R3 and the vector v = (1, 1, 1) in R3.…

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Q: Consider the three basic vectors: (2,1,0,-1),(-1,1,1,1),(2,7,4,1) a. give two vectors that are in…

A: Given the three basic vectors:                           (2,1,0,-1),(-1,1,1,1),and (2,7,4,1) We have…

Q: B = [(1, 2, 0)T, (1, 1, 1)T, (1, 0, 0T)] is an ordered basis for 3. a) Find [v]B, the coordinates of…

A: Given that B = 1 , 2 , 0T , 1 , 1 , 1T , 1 , 0, 0T is an ordered basis for ℝ3 .  We have to solve…

Q: Find the dimension and a basis of U = r2s+t 0 -3r s-t r, s, tER

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Q: The set B= {1-t,t-t,1- 2t-t} is a basis for P2. Find the coordinate vector of p(t) = 1+ 5t – 4t…

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Q: 3. Do the vectors (1, 1,0, 0), (1, -1,0,0), (0, 0, -1, 1) and (0, 0, -1, –1) form an orthogonal…

A: The solution is given as

Q: The set B={1+t, 2t-t, 1+t+t} is a basis for P₂. Find the coordinate vector of p(t)= -3+7t-7t…

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Q: Consider the orthogonal basis B = {e = (2, 2, –1); f = (2, –1, 2); g = (–1, 2, 2)}, determines the…

A: Given that B= {(2,2,-1),(2,-1,2),(-1,2,2)}. We need to find the coordinates of the vector (1,-1,0)…

Q: Let B = {1+t,1 – t} and C = {4, 1 + 5t, t²}. Does B form a basis for P2?

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Q: Show that B = {v1, v2, v3} is an orthogonal basis for R3: v1 = (3,−3,0), v2 = (2,2,−1), v3 =…

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Q: Consider the following two ordered bases of R³: B = - {(0, 1, 1), (0,2, −1), (1, −2, 1)}, с = {(2,…

A: a). Change of basis matrix from basis B to basis C.      a11 ​= −1/3​, a21 ​= 1/3​, and a31 ​= −1/3…