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Proving Lower Triangular Matrices When i > j
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[QUOTE="HMPARTICLE, post: 4975503, member: 511154"] Thanks, Ray. Maybe i should have made what i HAD done already a little more clear. I have already done what you said, regarding a 4x4 matrix and eliminating the first row and column, what results is another lower triangular matrix. the question asks me to show that that if i > j then ##B_{ij}## is a lower triangluar matrix. but in the 4 x 4 example, when i = j, ##B_{ij}## is a lower triangular still, so is proof by contradtiction not the way to go? in summary; I have found by experiment, when i = j, ##B_{ij}## is still lower triangular Also using a 4 x4 matrix as an experiment, when the first row and second column are deleted, what results is another lower triangular matrix. that is i < j finally, when the second row and the first column are deleted, that is i > j, now, this is not lower triangular, since the first row is a row of zeros. Prehaps I am not understanding the question, but what is evedent from experiment is that the opposite of what i have to prove is true. I hope my definition of a lower triangular is correct; that is, each entry to the right of the main diagonal is zero. That is where my confusion lies. [/QUOTE]
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Proving Lower Triangular Matrices When i > j
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