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InterviewSolution
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Let A be the set of all `3 xx 3` symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0. The number of matrices in A isA. 12B. 6C. 9D. 3 |
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Answer» Correct Answer - A A symmetric matrix is symmetric about its diagonal. So, there are even number of 1 and even number of 0 as off diagonal entries. Consequently, there can be either three 1 in the diagonal or one 1 and two zeros. Thus, we have the following cases: CASE I When diagonal elements are 1,1,1. In this case, we have Number of symmetric matrices = Number of arrangements of 1,0,0 as elements above the diagonal `=(3!)/(2!)=3` CASE II When diagonal elements are 1,0,0 ltbr. In this case, we have ltbRgt Number of symmetric matrices =(Number of arrangements of 1,0,0 as entries above the diagonal) `=(3!)/(2!)xx(3!)/(2!)=9` `:. " Total number of matrices in " A=3+9=12` |
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