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If `[a b c1-a]`is an idempotent matrix and `f(x)=x-^2=b c=1//4`, then the value of `1//f(a)`is ______. |
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Answer» Correct Answer - 0.25 `[(a,b),(c,1-a)]` is an idempotent matrix. `implies [(a,b),(c,1-a)]^(2)=[(a,b),(c,1-a)]` or `[(a,b),(c,1-a)][(a,b),(c,1-a)]=[(a,b),(c,1-a)]` or `[(a^(2)+bc,ab+b-ab),(ac+c-ac,bc+(1-a)^(2))]=[(a,b),(c,1-a)]` or `[(a^(2)+bc,b),(c,bc+(1-a)^(2))]=[(a,b),(c,1-a)]` or `a^(2)+bc=a` `a-a^(2)=bc=1//4` (given) `f(a)=1//4` |
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