Give solution

Asked by navjotsingh16082003 | 29th Mar, 2020, 04:37: PM

Expert Answer:

A is a triangular matrix means it is either upper triangular or lower triangular matrix
i.e. the entries either above the main diagonal or below the main diagonal are zero.
Therefore comma space straight l equals open parentheses 1 plus 2 plus 3 plus... plus straight n close parentheses plus 1 equals fraction numerator straight n left parenthesis straight n plus 1 right parenthesis over denominator 2 end fraction plus 1
Also comma space straight p equals minimum space number space of space zeroes space equals 1 plus 2 plus.... plus left parenthesis straight n minus 1 right parenthesis equals fraction numerator straight n left parenthesis straight n minus 1 right parenthesis over denominator 2 end fraction
If space straight A space is space straight a space diagonal space matrix comma space therefore space only space diagonal space entriez space are space non minus zero
therefore straight m equals straight n plus 1
Given colon space straight l plus 5 equals straight p plus 2 straight m
rightwards double arrow fraction numerator straight n left parenthesis straight n plus 1 right parenthesis over denominator 2 end fraction plus 1 plus 5 equals fraction numerator straight n left parenthesis straight n minus 1 right parenthesis over denominator 2 end fraction plus 2 left parenthesis straight n plus 1 right parenthesis
rightwards double arrow straight n squared plus straight n plus 12 equals straight n squared minus straight n plus 4 straight n plus 4
rightwards double arrow straight n plus 12 equals 3 straight n plus 4
rightwards double arrow straight n equals 4
Hence comma space the space order space of space matrix space straight A space is space 4 cross times 4.

Answered by Renu Varma | 30th Mar, 2020, 12:47: PM

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