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MidSol2

# MidSol2 - Comparing corresponding entries in the rst column...

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Comparing corresponding entries in the first column, we obtain a + b 3 = a c 3 and c + d 3 = a 3 + c , which gives b = c and d = a . In that case entries in the second column are automatically equal. We conclude that B has the form B = a c c a for arbitrary numbers a and c . As in class we conclude that this matrix represents the composition of a rotation and a dilation. To see this, it is enough to take r = a 2 + c 2 , and find an angle θ so that a = r cos θ , c = r sin θ . Then we have: B = r 0 0 r cos θ sin θ sin θ cos θ . 4. We perform the algorithm given in class: 1 1 1 | 1 0 0 3 2 0 | 0 1 0 0 0 1 | 0 0 1 subtract 3 times row I from row II 1 1 1 | 1 0 0 0 1 3 | 3 1 0 0 0 1 | 0 0 1 multiply row II by 1 1 1 1 | 1 0 0 0 1 3 | 3 1 0 0 0 1 | 0 0 1 subtract row II from row I 1 0 2 | 2 1 0 0 1 3 | 3 1 0 0 0 1 | 0 0 1
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