Let w, a,y, z be vectors and suppose z = -2x - 2y and w=2x+4y+ z. Mark the statements below that must be true. A. Span(x, y)-Span(w) B. Span(x, y) = Span(x, w, z) DC. Span(x, z)= Span(y, w) D. Span(y) = Span(w)

Let x, y, z be (non-zero) vectors and suppose w = 12x + 3y + 2z. If z = -4x - y, then w = C x+ Using the calculation above, mark the statements below that must be true. A. Span(w, z) = Span(x, z) B. Span(w, x, y) = Span(w, x, z) C. Span(w, x) = Span(x, y) D. Span(w, y) = Span(y, z) E. Span(w, y) = Span(w, z) y.

A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chessboard. On the second square, the King would place two grains of​ wheat, on the third​ square, four grains of​ wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining​ squares, how many grains of wheat should be placed on a square 16​? Also, find the total number of grains of wheat on the board at this time and their total weight in pounds.​ (Assume that each grain of wheat weighs​ 1/7000 pounds.)