Expansion by MinorsDate: 10/26/1999 at 23:22:26 From: Jessica Bullard Subject: How to evaluate determinants using expansion by minors How do you evaluate determinants using expansion by minors? |-3 0 6| | 6 5 -2| | 1 4 2| That's the problem originally. I tried doing the "T" thing where you take the -3 and place it outside the absolute value things, then draw a line through the 0, 6 across from it and the 6, 1 below it. Then place the rest of the numbers inside the absolute value things in the order they are in, but I don't know what to do from there... I know the answer should be 60 but I can't get that answer - I keep getting -174. Help me, please. Date: 10/27/1999 at 08:32:57 From: Doctor Jerry Subject: Re: How to evaluate determinants using expansion by minors Hi Jessica, It's best to use row operations first to produce more zeros, but you didn't mention that so I won't do it. Choose a column or row with the most zeros - the second column for example. Then the determinant is d = 0*(-1)*m0 + 5(+1)*m1 + 4(-1)*m2 where m0 = |6 -2| |1 2| = 12 - (-2) = 14 (We didn't need to compute this minor, since it'll be multiplied by 0) m1 = |-3 6| | 1 2| = -6 - 6 = -12 and m2 = |-3 6| | 6 -2| = 6 - 36 = -30 So, d = 0*(-1)*m0 + 5(+1)*m1 + 4(-1)*m2 = 0*(14) + 5(-12) - 4(-30) = 0 - 60 + 120 = 60 - Doctor Jerry, The Math Forum http://mathforum.org/dr.math/ |
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