7. (a) (b) (c) For the subspace S = span Find a basis for St. -1 a) Find projsu? 2 1 0 Determine if u = -3 is in S? 1] " 2 -3 2

Q: Let v1 vector=[−4  h] and v2 vector =[−10   20]   (check image for reference) Then span(v1…

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Q: iii) The area of the parallelogram spanned by the three-dimensional vectors 3 -4 and 2 -5 is Number

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Q: Determine if the list ( [111], [121], [011], [122] ) of vectors from vector space V = R^3 is…

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Q: Compute the orthogonal projection of v = proj, (v) = -5 onto the line L through -4 and the origin. 6…

A: Introduction:  The vector projection of a vector a on (or onto) a nonzero vector b, sometimes…

Q: D = 3 u=(9,-4); || u || = -√97 u=(9,-4): || u ||= √97 u=(9,4): ||u||= -√97 u= (9,4); ||u||= √97

A: given u has initial point P at (0,0) and terminal point Q at (9,-4)

Q: a. Write the solution set to the following equation in parametric vector form (consider ₁ to be the…

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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 +…

A: Given  T(v1,v2,v3) = (4v2-v1,4v1+5v2)Image of v is given by T(1,-2,-4) = (-9,-6) hence (a). the…

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

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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, 4v, +…

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Q: Find a linear mapping G that maps [0, 1] × [0, 1] to the parallelogram in the xy-plane spanned by…

A: The linear map G maps  to the parallelogram in XY-plane.The parallelogram is spanned by the vectors…

Q: (1 point) Are the vectors u = [152], [-5 1 -4 and w= -21 25 -28] linearly independent? Choose If…

A: The vectors u→,v→,w→ are said to be linear independent if au→+bv→+cw→=0 for a=0,b=0,c=0 The vectors…