If a, b, c > 0 , and , x, y, z ∈ R , then determinant left|{begin{array}{*{20}{c}}{{{left( {{a^

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3 and 4 .Determinants and Matrices

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If $a, b, c > 0 \, and \, x, y, z \in R$ , then the determinant $\left|{\begin{array}{*{20}{c}}{{{\left( {{a^x}\, + \,\,{a^{ - x}}} \right)}^2}}&{{{\left( {{a^x}\, - \,\,{a^{ - x}}} \right)}^2}}&1\\{{{\left( {{b^y}\, + \,\,{b^{ - y}}} \right)}^2}}&{{{\left( {{b^y}\, - \,\,{b^{ - y}}} \right)}^2}}&1\\{{{\left( {{c^z}\, + \,\,{c^{ - z}}} \right)}^2}}&{{{\left( {{c^z}\, - \,\,{c^{ - z}}} \right)}^2}}&1\end{array}} \right|$ $=$

A

$a^xb^yc^z$

B

$a^{-x}b^{-y}c^{-z}$

C

$a^{2x}b^{2y}c^{2z}$

D

zero

Solution

$C_1 \rightarrow C_1 – C_2$ and take $4$ common

==> two identical columns

Standard 12

Mathematics

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