Comparing corresponding entries in the first column, we obtaina+b√3 =a−c√3 andc+d√3 =a√3 +c, which givesb=−candd=a. In that case entries in the secondcolumn are automatically equal. We conclude thatBhas the formB=a−ccafor arbitrary numbersaandc.As in class we conclude that this matrix represents the composition of a rotation anda dilation. To see this, it is enough to taker=√a2+c2, and find an angleθso thata=rcosθ,c=rsinθ. Then we have:B=r00rcosθ−sinθsinθcosθ.4. We perform the algorithm given in class:⎛⎝111|100320|010001|001⎞⎠subtract 3 times row I from row II⎛⎝111|1000−1−3|−310001|001⎞⎠multiply row II by−1⎛⎝111|100013|3−10001|001⎞⎠subtract row II from row I⎛⎝10−2|−210013|3−10001|001⎞
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