InterviewSolution
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InterviewSolution
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Let A be the set of all `3xx3` symmetric matrices all of whose either 0 or 1. Five of these entries are 1 and four of them are 0. The number of matrices A in A for which the system of linear equations `A[(x),(y),(z)]=[(1),(0),(0)]` has a unique solution isA. less than 4B. at least 4 but less than 7C. at least 7 but less than 10D. at leat 10 |
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Answer» Correct Answer - B `[(0,a,b),(a,0,c),(b,c,1)]` Either `b=0` or `c=0implies |A| ne 0` `implies` two matrices `A=[(0,a,b),(a,1,c),(b,c,0)]` Either `a=0` or `c=0 implies |A| ne 0` `implies` two matrices `A=[(1,a,b),(a,0,c),(b,c,0)]` Either `a=0` or `b=0implies |A| ne 0` `implies` two matrices `A=[(1,a,b),(a,1,c),(b,c,1)]` `a=b=0 implies |A|=0` `a=c=0 implies |A|=0` `b=c=0 implies |A| =0` Therefore, there will be only six matrices. |
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