31 4 Consider R³ with dot product and Euclidean norm, a subspace U, vector x defined below. Compute the orthogonal projection Пlu(x) of x onto U, a distance d(x, U) from x onto U. Include necessary tableau work for linear indepe and/or solving system(s) of linear equations. U = span[u₁ u2= x= 0 5

Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}

Find a linear map 7 that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the vectors (6,5) and (7,4). (Give your answer in the form (*, *). Express numbers in exact form. Use symbolic notation and fractions where needed.) T(u, v) = (6u+7v,5u +4v) Calculate the double integral of e2x-over P via change of variables. (Express numbers in exact form. Use symbolic notation and fractions where needed.) 1/₂ 2²x-A= Incorrect 10 ½ (e¹⁰ − 1)(e² - 1) 70 CA

Is this set of vectors span a line or all of R2?