The vector x is in a subspace H with a basis B = {b₁,b₂). Find the B-coordinate vector of x. 2 b₁ = *-(-3) -(¯)--[-2] b₂ = X= 5 [X] = 6

Q: Let x(¹) (t) = = -3t e 4e-3t, 0 0 x (²) (t) = [_5e-31]. -5e-3t, 0 Are the vectors x(¹) (t), x(²) (t)…

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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: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

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Q: Find a vector equation for the line through the point (4, 5, -1) perpendicular to the vectors , 6,…

A: we have to find the line equation passing through point (4,5,-1) and perpendicular to the vectors…

Q: Let m = (-3,1,5) and n = (5,-1,2). calculate the vector p = n - ((m*n)/(m*m))*m.

A: here we get p=0

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Q: Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2,…

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Q: Find the vector X (in standard coordinates) determined by the given coordinate vector [X] and the…

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Q: Find all vectors u such that ux(1,1,1)=(8,-5,-3).

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Q: (i) Prove that { (1, 2, 1) , (2, 1, 5) , (1, –4, 7) } is linear dependent subset of R³. (ii)…

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Q: Find the vector in component form with initial poi

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Q: Find the vector x determined by the given coordinate vector [x] and the given basis B. 8= 6 -6 X =…

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Q: Are the vectors = [−5_3 −1], v = [02-1] and w = [-25 21 -8] linearly independent? Choose If they are…

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

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Q: Find the coordinate vector (v)s relative to the basis S= {v ,,v,,v;} 21 for v = (2, 1, -2), if V=…

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