Consider the vector space R and the function (1,y) = 38191 +42242 +2343, for x = (11,12,13), y = (91-92, 93) ER?. (a) Sh

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Consider The Vector Space R And The Function 1 Y 38191 42242 2343 For X 11 12 13 Y 91 92 93 Er A Sh 1 (23.3 KiB) Viewed 26 times

Consider the vector space R and the function (1,y) = 38191 +42242 +2343, for x = (11,12,13), y = (91-92, 93) ER?. (a) Show that the given function (;-) defines an inner product on R3. 7 7 221 V21 (b) Show that B = is an orthonormal basis of 21 Span(B) with respect to the inner product (-). (3 combination of the vectors in B. (a) Find a basis for the orthogonal complement of {(-2,3,1)} with respect to the inner product (). 14 {(*)(**»)} . (c) The vector w = (3.5") belongs to Span(B). Using (b), write w as a linear