InterviewSolution
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InterviewSolution
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show that the determinant `|{:(a^(2)+b^(2)+c^(2),,bc+ca+ab,,bc+ca+ab),(bc+ca+ab,,a^(2)+b^(2)+c^(2),,bc+ca+ab),(bc+ca+ab,,bc+ca+ab,,a^(2)+b^(2)+c^(2)):}|` is always non- negative. |
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Answer» `|{:(a^(2)+b^(2)+c^(2),,bc+ca+ab,,bc+ca+ab),(bc+ca+ab,,a^(2)+b^(2)+c^(2),,bc+ca+ab),(bc+ca+ab,,bc+ca+ab,,a^(2)+b^(2)+c^(2)):}|` `=|underset(c" "a" "b)underset(b" "c" "a)(a" "b" "c)||underset(c" "a" "b)underset(b" "c" "a)(a" "b" "c)|` Which is always non-negative. |
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