By the Gram-Schmidt process, obtain an orthonormal basis for R³ from the ordered basis given by --0--0-0) = 1, = 1 =

(i) Give an example of two orthonormal vectors in R³. (ii) Using C=9 D=3 E=5 F=4 Schmidt process to find an orthonormal basis from the initial vectors () and (7). use the Gram- (iii) Construct a matrix which implements a shear of factor 3 along the first vector of your basis constructed in (ii), in that basis. Then use change of basis methods to give the corresponding (similar) matrix in the standard basis of R². Homework

Find a basis for Q(3^(1/3), 3^(1/2)) over Q.

Find the coordinate matrix of x relative to the orthonormal basis B in R". x = (10, 20, 5), B = {G) (-), (0, o, 1)} [x]g = 1 1