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340spring06exam1sol - TOTAL SCORE(90 points possible MATH...

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Unformatted text preview: TOTAL SCORE (90 points possible): MATH 340; EXAM # 1, February 28, 2005 (R.A.Brualdi) Discussion Section ( circle one ): Mon 8:50 Mon 12:05 Wed 8:50 Wed 12:05 Name: These R. Solutions 1. (12 points) Let A be the matrix 1 2 3 4 2 4 1 3 3 5 1 2 . Let x be a 4 × 1 matrix (a column vector) ( x 1 , x 2 , x 3 , x 4 ) T , let y be a 1 × 3 matrix ( y 1 , y 2 , y 3 ). (i) Express Ax as a linear combination of the columns of A : x 1 1 2 3 + x 2 2 4 5 + x 3 3 1 1 + x 4 4 3 2 (ii) Express yA as a linear combination of the rows of A : y 1 bracketleftBig 1 2 3 4 bracketrightBig + y 2 bracketleftBig 2 4 1 3 bracketrightBig + y 3 bracketleftBig 3 5 1 2 bracketrightBig (iii) Is yAx in the row space, column space, both the row and column space or neither? Circle one. NEITHER : yAx is a scalar (a 1 × 1 matrix). 2. (14 points) Let A be a 4 × 3 matrix. (i) Let E be the elementary matrix such that EA interchanges rows 2 and 4 of A . What is E and, if E is invertible, what is the inverse of E ?...
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340spring06exam1sol - TOTAL SCORE(90 points possible MATH...

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