Question

8. Let S = {x_1, ..., x_n} be an orthonormal basis in an inner-product space V. Find <?_{i=1}^n ix_i, ?_{i=1}^n x_i>. 9. Use Gram-Schmidt process to find an orthogonal basis of the row space of A where A = egin{pmatrix} 1 & 0 & -1 \ 1 & 1 & 1 \ -1 & 1 & 0 \ 1 & 0 & 1 end{pmatrix}. 10. Let E = [1, x, x^2] be the standard ordered basis for P_3 and consider the inner product <p(x), q(x)> = int_0^1 p(x)q(x)dx. Use Gram-Schmidt process to convert E to an orthonormal basis for P_3.

          8. Let S = {x_1, ..., x_n} be an orthonormal basis in an inner-product space V. Find <?_{i=1}^n ix_i, ?_{i=1}^n x_i>.

9. Use Gram-Schmidt process to find an orthogonal basis of the row space of A where A = egin{pmatrix} 1 & 0 & -1 \ 1 & 1 & 1 \ -1 & 1 & 0 \ 1 & 0 & 1 end{pmatrix}.

10. Let E = [1, x, x^2] be the standard ordered basis for P_3 and consider the inner product <p(x), q(x)> = int_0^1 p(x)q(x)dx. Use Gram-Schmidt process to convert E to an orthonormal basis for P_3.

8. Let S = x1, ..., xn be an orthonormal basis in an inner-product space V. Find <?i=1^n ixi, ?i=1^n xi>.

9. Use Gram-Schmidt process to find an orthogonal basis of the row space of A where A = eginpmatrix 1 0 -1 1 1 1 -1 1 0 1 0 1 endpmatrix.

10. Let E = [1, x, x^2] be the standard ordered basis for P3 and consider the inner product <p(x), q(x)> = int0^1 p(x)q(x)dx. Use Gram-Schmidt process to convert E to an orthonormal basis for P3.

Added by Aitor P.

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