4. Consider the vector space R3 and the function (x, y) = 3c1y1 + 4.62y2 + x3y3, for x = (21, 22, 23), y = (41, 42, 43)

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4 Consider The Vector Space R3 And The Function X Y 3c1y1 4 62y2 X3y3 For X 21 22 23 Y 41 42 43 1 (62.65 KiB) Viewed 21 times

4. Consider the vector space R3 and the function (x, y) = 3c1y1 + 4.62y2 + x3y3, for x = (21, 22, 23), y = (41, 42, 43) € R. Show that the given function (3) defines an inner product on R3. (a) 2V21 V21 (b) = 9 {**:0).( } (3, -5.0) belongs to Span(B). Using (b), write w as a linear Show that B is an orthonormal basis of 7 21 14 Span(B) with respect to the inner product (,). 1 The vector w = , combination of the vectors in B. Find a basis for the orthogonal complement of {(-2,3,1)} with respect to the inner product (;-). (c) (a)