For X = (X, X2, X3), = (y, Y2, Y3) ER , define an inner...

 

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For X = (X₁, X2, X3), ỷ = (y₁, Y2, Y3) ER ³, define an inner product on R³ by: (x, y) = x₁y1 + 2x2y2 + 3x3y3. (a) Let B = {(1, 1, 1), (1,1,0), (1,0,0)} be a basis for R ³. Use the Gram-Schmidt procedure to turn B into an orthonormal basis. (b) Find [x], where x = (0, 2, 4) and B" is the orthonormal basis found in (a). For X = (X₁, X2, X3), ỷ = (y₁, Y2, Y3) ER ³, define an inner product on R³ by: (x, y) = x₁y1 + 2x2y2 + 3x3y3. (a) Let B = {(1, 1, 1), (1,1,0), (1,0,0)} be a basis for R ³. Use the Gram-Schmidt procedure to turn B into an orthonormal basis. (b) Find [x], where x = (0, 2, 4) and B" is the orthonormal basis found in (a).

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a To turn the basis B 1 1 1 1 1 0 1 0 0 into an orthonormal basis we can use the GramSchmidt procedure Step 1 Normalize the first vector in B v 1 1 1 ... View the full answer