1) Let B = be an orthogonal basis, y = and let W = span(B). %3! A) Calculate the orthogonal projection of y onto W using two different methods. t B) Determine the shortest distance from y to W and the shortest point in W closes to y. E C) Let a = Show c = a+band ||c|? = ||a||? + ||b||², but neither a nor b and c = %3D are orthogonal projections of c onto W.E

Q: 1. Define the vectors and as below, ²-[3] *-3 (a) Show that the vectors form a linearly independent…

A: The given vectors are  u→=2-1, v→=13 We have to show that the vectors form a linearly independent…

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A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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A: NOTE- AS WE ARE ALLOWED TO ANSWER ONE QUESTION WITH THREE SUBPARTS IN ONE SESSION SO, I HAVE…

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A: First calculate the vector 3a + b and than devide it with its magnitude for unit vector.

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A: [2].

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A: Note:  Since you have posted multiple questions, we will solve first question for you. Kindly repost…

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A: According to our terms and conditions I have solved first part for next question repost

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A: A vector having length u→ and makes an angle θ is given by  u→ = u→cosθ i^ + u→sinθ j^

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A: GIVEN SETS : The given sets are : 120,123 The augmented matrix is : 120123R2→R2-R1~120003

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