MATH 551 Midterm: Kansas State MATH 551 551t1s99

Consider the following elements of R^3. x = [1 2 1], y = [1 3 2], z = [1 1 0], w = [3 8 5]. Show that Span{x, y} = Span{z, w).

Which of the following sets of vectors span R_2? [1 4], [-1 1] spans R_2 does not span R_2 [0 0], [1 1], [-2 -2] spans R_2 does not span R_2 [1 2], [2 -2], [0 2] spans R_2 does not span R_2 [6 12], [-3 6] spans R_2 does not span R_2

Solve the following problems, showing any necessary work. [1 point] Let S ={[-3 0 0 2] , [-1 1 2 0], [-4 0 2 2]}. Determine which of the following vectors are in the linear span of S: [1 1 4 -2], [-3 1 1 -3], [3 1 0 -2]