Prove that if A is upper triangular and B is the matrix

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SUMMARY

If matrix A is upper triangular and matrix B is formed by deleting the ith row and jth column of A, then B remains upper triangular when i < j. This conclusion can be established through mathematical induction. By verifying the property for small values of n (specifically n = 2, 3, and 4), one can effectively generalize the inductive step to prove the statement for all n.

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How to prove that if A is upper triangular and B is the matrix that results when the ith row and jth column of A are deleted, then B is upper triangular if i<j.
 
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It seems like induction could work here. Have you tried it.? . Try showing it

works for small values of n, say , 2,3,4 , and see how to generalize for the

inductive step.
 

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