Use least squares to find the orthogonal projection of u onto the subspace of Rª spanned by the vectors V₁, V2, and v3, where u = (0, 8, 6, 0), V₁ = (3, 0, 0, 1), v2 = (0, 1,-1,0), V3 = = (1,1,0, -3).

Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar

A: We can check whether the three vectors are co planar  or not as below

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: The normal vector to the vectors u = (2, 1, 1) and v = (1, -1, 3) is:    4i - 5j + 3k  4i - 5j -…

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Q: Find all vectors in R' that are perpendicular to both [1,0, 1, 0] and [1,2,0, 1] and then find a…

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Q: Show that v, = (1,0,–1) , v, = (1,0,1) , v3 = (1,1,1) span R’. %3D Express vector v= (4,2, 2) as…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Determine whether the vectors v₁ = (1, 6, 0, 0), v₂ = (0, -1, 0, 1), v3 = (0, 0, 1, 1), and v₁ = (1,…

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Q: Find the change-of-coordinate matrix P from B to C and P from C to B for the bases B = {1,t,t^2} and…

A: Let U={u1,u2,⋯,un} and V={v1,v2,⋯,vn} are two bases of a vector space W.The identity map I:W→W…

Q: Determine which set of vectors is linearly dependent (a) (b) , (c) (d) (e) (f) O (a) O (b) O (c) O…

A: Recall:A set of vectors is said to be linearly dependent if the determinant is zero.If the…

Q: Can you provide a sketch or model of the vector function (x,y,1-(x+y)) and show it passing through…

A: The sketch can be plotted using 3D modelling tools. In the modelling tool, select the appropriate…

Q: Apply Gram-Schmidt orthogonalization to the column vectors of A, a1 = (1, 1, 0)T ,a2 = (1, 0, 1)T ;…

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Q: b) u = (3, -1), v = (1, 5) et w = (8, -2) c) i = (1, 0, 0), j = (0, 1, 0) et k = (0, 0, 1) gajte…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Given, A=( 1,1,0 ); B=( -2,3,-4 ); P=( -3,1,6 )To find: Distance from point P to the line through A…

Q: Given any linearly independent set of vectors V = {v, V2, , }, prove that there is at least one…

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Q: Ui=(1, 1, 1, -1) Uz=(5, 1, 1, 1) Uз-(-3, -3, 1, -3)

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Q: Determine the vector projection of the vector (5,0, 7) on the vector (–1,3,4).

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Q: Use matrix multiplication to find the orthogonal projection of (-8, 5, 7) on the xy-plane. Let T…

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Q: Show that VI = (1,0,1) , v, = (1,1,0) , v3 = (1,1,1) span R'. Express vector v= (2, 1, 3) as linear…

A: v1 ,v2 ,v3 ,...,vn span R^n if det(v1,v2,...,vn) is non zero

Q: Which of the following sets of vectors in R' are linearly independent? (a) (-3,0,4), (5,-1,2),…

A: Linearly independent set: The set of vectors x1, x2, ..., xn in a vector space V is said to be…

Q: Let x=(1,2,3) and y=(0,1,2) Find projyX. Find projection of Y onto column space A= [(1,0); (3,2);…

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Q: 2. Consider the vectors [2, 1,0, 0], [3, 1, 0, 0], [0, 0,0, 1)] in R'. Find a vector v so that v,…

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