MATH348 - September 30, 2009 NAME:
Exam I - 50 Points SECTION:
In order to receive full credit, SHOW ALL YOUR WORK. Full credit will be given only if all
reasoning and work is provided. When applicable, please enclose your final answers in boxes.
1. (10 Points) Short Answer - Justify your response.
(a) Suppose that Ax =b, where A∈Rn×n, has no solutions. What can be said about solutions to Ax =0?
(b) Suppose that det(A) = 0. Could there exist a solution to Ax =bfor some b∈Rn?
(c) Suppose that the column space of An×nis precisely Rn. What can be said about solutions to Ax =0?
(d) Suppose that λ= 0 is an eigenvalue of A. What can be said about solutions to Ax =0?
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