Take the function on the vector space R3. = 3x₁y₁+4x2y2+x3y3 Where X = (X1, X2, X3) y = (y₁, y2, y3) The given func

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Take The Function On The Vector Space R3 X Y 3x Y 4x2y2 X3y3 Where X X1 X2 X3 Y Y Y2 Y3 The Given Func 1 (37.52 KiB) Viewed 34 times

Take the function on the vector space R3. <x,y>= 3x₁y₁+4x2y2+x3y3 Where X = (X1, X2, X3) y = (y₁, y2, y3) The given function<x,y> defines an inner product on R3. 2√21 √21 a.) Show that C = 7,0), (212¹, -2, 0) } is an orthonormal basis of Span(C) with 14 respect to the inner product < x,y> (1 point) b.) z=(3, -1/2, 0) is a vector which belongs to Span(C). Using the answer from (a), write z as a linear combination of the vectors in C. (2 points)