InterviewSolution
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InterviewSolution
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If, Si = a^i + b^i + c^i then what is the value of \(\begin{vmatrix}S0 & S1 & S2 \\S1 & S2 & S3 \\S2 & S3 & S4 \end {vmatrix}\)?(a) (a + b)^2(b – c)^2(c – a)^2(b) (a – b)^2(b – c)^2(c + a)^2(c) (a – b)^2(b – c)^2(c – a)^2(d) (a – b)^2(b + c)^2(c – a)^2The question was posed to me in an interview for job.Asked question is from Application of Determinants topic in portion Determinants of Mathematics – Class 12 |
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Answer» RIGHT CHOICE is (c) (a – b)^2(b – c)^2(c – a)^2 The best explanation: We have, \(\begin{vmatrix}1 & 1 & 1 \\a & b & c \\a^2 & b^2 & c^2 \end {vmatrix}\) So, the value of the \(\begin{vmatrix}1 & 1 & 1 \\a & b & c \\a^2 & b^2 & c^2 \end {vmatrix}\) = (a – b)(b – c)(c – a) Now, by circulant determinant, \(\begin{vmatrix}1 & 1 & 1 \\a & b & c \\a^2 & b^2 & c^2 \end {vmatrix}\) X \(\begin{vmatrix}1 & 1 & 1 \\a & b & c \\a^2 & b^2 & c^2 \end {vmatrix}\) = \(\begin{vmatrix}S0 & S1 & S2 \\S1 & S2 & S3 \\S2 & S3 & S4 \end {vmatrix}\) Multiplying the determinant in row by row, We get, (a – b)^2(b – c)^2(c – a)^2 |
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