CHEM 471 Midterm: CHEM 471 UMass Amherst Midterm key 2006
Document Summary
Spring 2014: (18 points) you are given below the matrix a together with its row reduced echelon form c. Note: you do not have to check that a and c are indeed row equivalent: determine the rank of a. Explain how it is determined by the matrix c: find a basis for the kernel ker(a) of a. Justify your answer: find a basis for the image im(a) of a. Justify your answer: let b be the basis you found in part 1c for the image of a and let ~a6 be the sixth column of a. Find the b-coordinate vector [~a6]b of ~a6: (12 points) for which values of the constant k do the vectors below form a basis of r3. 7 k: (16 points) let ~v1 be a non-zero vector in r2. Recall that the re ection t : r2 . R2, with respect to the line spanned by ~v1, is given by.
