MATH 2550 Midterm: MATH 2550 Iowa Exam 2
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Find the standard matrix for the linear transformation t de ned by the formula. T ((x1, x2)) = (5x1 + 3x2, x1 4x2, x2, 0). Find three vectors which are in the image of t . Find two vectors in the codomain of t which are not in the image of t . Find a basis for the column space of a. Find a basis for the row space of a. Find a basis for the nullspace of a. Write one of the columns of a as a linear combination of the other columns of a. Write as 1 8t + 5t2 as a linear combination of 1 + 4t 3t2 and 2 + 5t 4t2. [4] 4a. ) (2, 0, 1, 3) (5, 4, 8, 2) = Circle the correct answer and ll in the blank if appropriate. Suppose that a is a 4 4 matrix, rank(a) = 4, and rank[a|b] = 4.
