MATH 21A Midterm: MATH 20 Harvard 2004Spring20MidtermII sol
Document Summary
Full credit may not be given for an answer alone. You may use the backs of the pages or the extra pages for scratch work. Students who, for whatever reason, submit work not their own will ordinarily be required to withdraw from the college. In all situations where row operations are performed on a matrix, label each operation to receive partial credit in case of arithmetic mistakes. 1: (15 points) let w be the subspace spanned by. Find a basis for w and the dimension of w . The reduced row echelon form of a is. Since r1 and r3 form a basis col r, we must have that a1 and a3 form a basis for col a. 2: (15 points) find all numbers c such that. By expanding along the bottom row, we see the determinant of this matrix is. Thus 3 and 5 are the values of c which make this matrix noninvertible.
