MATH-205 Midterm: Bates MATH 205 111309ross205examsoln
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In this problem, assume a and b are 4 x 4 square matrires. Suppose: rref(a)= r where r has exactly three leading-l"s, rref(b)= s and s = 14. In the left margin, next to each statement, write "t" if the statement is it always true and" f" if it"s not always true, for any such matrices a and b. T b) the determinant of b is non-zero. f cj the equation ax ~ b hasin6niteiymanyoolutionsx foreachb e~4. /jri cap! d-< ~ ire";j- ~ fite. (i/v ~f/";". l. wf. I: the number 0 is an eigenvalue for a. F h) the numbec 0 is an eigenvalue for b. "6 ~ x~ 0 i ~ 0fi~rkdy /(1 ;1/v/ (11) k. ~ ]i/io~. T j) a and b are not row equivalent. T k) a and b are not similar. s~ d c; q"j1ej vtjj 11mtf n. t it. T 1)in any basis of nul(a), there is exactly one vector.
