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Unformatted text preview: MAT223 Final
Note: I’ll write column vectors horizontally and with commas sometimes, to save space.
1. (2). If k = 2 the last equation disappears and the system has inﬁnitely many solutions.
For any other values of k , the last equation simpliﬁes to (k + 2)x3 = 1. This is inconsist
with the second equation unless k + 2 = 2 , in which case again the system has inﬁnitely
2. (4). B is true because det A2 = (det A)2. D is equivalent to dim(row A) = 0,...
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