Find the dimension of the subspace U = span{[1, 1, 1], [2, 5, 2], [1, 2, 3]}.Select one:a. 1b. none of the other choices is truec. 3d. 2

Let be U = Span{[3,0,1]} a subspace of W=Span{[1,0,0],[1,0,1]}, and the space V the orthogonal complement of U. Answer these two following questions:1. Give a basis v=[ , , ] for V,2. Give dim V = .(If your result is not an integer, then please give your result with 2 decimals (rounded - not cut-off; use a dot as a decimal separator))

Let A be a 3 x 5 matrix. If dim(null(A))=2, then the dimension of the column space of A isSelect one:a. 3b. 1c. 2d. None of the other choices is correct

Determine whether the set S spans R3. If the set does not span R3, then give a geometric description of the subspace that it does span.S = {(1, 0, 3), (2, 0, −1), (4, 0, 5), (2, 0, 6)}

Which of the following are subspaces of R3 ?(i) {(x,y,z)| z = 2x+3y+2}(ii) {(x,y,z)| x2+y2=z2}Select one:a. (ii) onlyb. (i) and (ii)c. None of the other choices is correctd. (i) only

Which of the following sets spans the vector spaceR3? Select all that apply. A. ⎧⎩⎨⎪⎪⎡⎣⎢211⎤⎦⎥,⎡⎣⎢301⎤⎦⎥,⎡⎣⎢512⎤⎦⎥,⎡⎣⎢602⎤⎦⎥⎫⎭⎬⎪⎪ B. ⎧⎩⎨⎪⎪⎡⎣⎢110⎤⎦⎥,⎡⎣⎢300⎤⎦⎥⎫⎭⎬⎪⎪ C. ⎧⎩⎨⎪⎪⎡⎣⎢201⎤⎦⎥,⎡⎣⎢110⎤⎦⎥,⎡⎣⎢001⎤⎦⎥⎫⎭⎬⎪⎪ D. ⎧⎩⎨⎪⎪⎡⎣⎢100⎤⎦⎥,⎡⎣⎢012⎤⎦⎥,⎡⎣⎢003⎤⎦⎥⎫⎭⎬⎪⎪