Problem 10 - Consider subspace S = {(x, y, z) |x + y + z = 0} of R³ and two bases B and C for S given by B = {(2,0,-2),

[answerhappygod]

Problem 10 Consider Subspace S X Y Z X Y Z 0 Of R And Two Bases B And C For S Given By B 2 0 2 1 (29.93 KiB) Viewed 46 times

Problem 10 - Consider subspace S = {(x, y, z) |x + y + z = 0} of R³ and two bases B and C for S given by B = {(2,0,-2), (0,3,-3)} and C = {(1, 1,-2), (-2, 1, 1)}. Let us consider two vectors and 7 in the plane S: = (-2,5,-3) and 7 = (3,3, -6). A. Calculate the coordinates of 5u-37 in B and C, i.e., Coords(5u-37, B) and Coords(5ũ-30, C). B. An orthogonal basis for S is O = {(1,-1,0), (1, 1,-2)}. Obtain an orthonormal basis N for S using O and then calculate Coords(u, N) and Coords(5, N). C. Obtain the dot product of u and using Coords(u, N) and Coords(7, N).