MATH 2550 Midterm: MATH 2550 Iowa Exam 2Spring2014Solutions 1
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Math 2550 matrix algebra exam #2 (form a) Use cramer"s rule to solve the following system of equations for y. You do not need to solve for x or z. = 5(3 + 8) + 2(9 2) = 55 + 14 = 41 or equivalently: = 3(5 6) + 2( 20 2) = 3 44 = 41. 1 (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) replacing 2nd column: = 2(30 0) = 10(0 6) = 60. = e4t( 6e 3t) 4e4t(2e 3t) = 6et 8et = 14et. Does the matrix d have an inverse? yes. Are the columns of d linearly independent? yes. Are the rows of d linearly independent? yes. D 1dx = d 1(cid:20) 0 x = (cid:20) 3e 4t. = (1 )2 36 = 2 2 35 = ( + 5)( 7) = 0. 1(cid:21) x2 x2 (cid:21) = (cid:20) 1 x2(cid:21) = (cid:20) x2. = 7: (cid:20) 6 x2(cid:21) = (cid:20) x2.
