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Unformatted text preview: s and verify by matrix multiplication that s satises the equation Ax = b . (c) Write b as a linear combination of the columns in A . Problem 5 Let E = 1 0 0 0 1 0 3 0 1 and let A be an arbitrary 3 3 matrix. (a) Describe the rows of EA in terms of the rows of A . (b) Describe the columns of AE in terms of the columns of A . Problem 6 Let e j denote the j th unit column that contains a 1 in the j th position and zeros everywhere else. For a general matrix A n n , describe the following products. (a) Ae j (b) e T i A (c) e T i Ae j Problem 7 Suppose that A and B are m n matrices. If Ax = Bx holds for all n 1 columns x , prove that A = B . Hint: What happens when x is a unit column? 3...
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