6. Show that the product of lower (resp. upper) triangular matrices is lower (resp. upper) triangular....

 

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6. Show that the product of lower (resp. upper) triangular matrices is lower (resp. upper) triangular. Show that if a lower (resp. upper) triangular matrix is invertible, then its inverse is lower (resp. upper) triangular. Hint: Induction for each? 7. Suppose B is produced from A by swapping rows 1 and 2 of A, and that A is invertible. We know row operations do not disturb invertibility. How would we produce B-1 from A-? 6. Show that the product of lower (resp. upper) triangular matrices is lower (resp. upper) triangular. Show that if a lower (resp. upper) triangular matrix is invertible, then its inverse is lower (resp. upper) triangular. Hint: Induction for each? 7. Suppose B is produced from A by swapping rows 1 and 2 of A, and that A is invertible. We know row operations do not disturb invertibility. How would we produce B-1 from A-?

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To prove that the product of lower triangular matrices is lower triangular we will use mathematical induction First lets define the terms A lower triangular matrix is a square matrix where all the ent... View the full answer