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# 7. Consider the Theorem: Suppose A and B are two lower triangular matrices (Defined in 8...

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###### 7. Consider the Theorem: Suppose A and B are two lower triangular matrices (Defined in 8...

7. Consider the Theorem: Suppose A and B are two lower triangular matrices (Defined in 8 3.1), of order n. Then, the product AB is also a lower triangular matrix. Likewise for upper triangular matrices. (We say that the set of lower triangular matrices, of order n, is closed under multiplication.) Prove this theorem, for n = 3, by multiplying the following two matri- ces: a1 0 0 A bi b 0 1 0 0 and B 2 0 21 22 23 Answer: AB-

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