The value of $\left| {\,\begin{array}{*{20}{c}}{{5^2}}&{{5^3}}&{{5^4}}\\{{5^3}}&{{5^4}}&{{5^5}}\\{{5^4}}&{{5^5}}&{{5^7}}\end{array}\,} \right|$ is
The value of $\left| {\,\begin{array}{*{20}{c}}{{5^2}}&{{5^3}}&{{5^4}}\\{{5^3}}&{{5^4}}&{{5^5}}\\{{5^4}}&{{5^5}}&{{5^7}}\end{array}\,} \right|$ is
- A
${5^2}$
- B
$0$
- C
${5^{13}}$
- D
${5^9}$
Similar Questions
If $a, b, c$ are all different and $\left| {\begin{array}{*{20}{c}}a&{{a^3}}&{{a^4}\, - \,1}\\b&{{b^3}}&{{b^4}\, - \,1}\\c&{{c^3}}&{{c^4}\, - \,1}\end{array}} \right|$ $= 0$ , then :
The value of the determinant $\left| {\,\begin{array}{*{20}{c}}a&{a\, + \,b}&{a\, + \,2b}\\{a\, + \,2b}&a&{a\, + \,b}\\{a\, + \,b}&{a\, + \,2b}&a\end{array}\,} \right|$ is
If $a, b, c$ are all different from zero and $\left| {\begin{array}{*{20}{c}} {1 + a}&1&1\\ 1&{1 + b}&1\\ 1&1&{1 + c} \end{array}} \right| = 0$ , then the value of $a^{-1} + b^{-1} + c^{-1}$ is
If $a, b, c$ are all different from zero and $\left| {\begin{array}{*{20}{c}} {1 + a}&1&1\\ 1&{1 + b}&1\\ 1&1&{1 + c} \end{array}} \right| = 0$ , then the value of $a^{-1} + b^{-1} + c^{-1}$ is
If $f(x) = \left| {\begin{array}{*{20}{c}}1&x&{x + 1}\\{2x}&{x(x - 1)}&{(x + 1)x}\\{3x(x - 1)}&{x(x - 1)(x - 2)}&{(x + 1)x(x - 1)}\end{array}} \right|$ then $f(100)$ is equal to
If $f(x) = \left| {\begin{array}{*{20}{c}}1&x&{x + 1}\\{2x}&{x(x - 1)}&{(x + 1)x}\\{3x(x - 1)}&{x(x - 1)(x - 2)}&{(x + 1)x(x - 1)}\end{array}} \right|$ then $f(100)$ is equal to
- [IIT 1999]
By using properties of determinants, show that:
$\left|\begin{array}{ccc}1+a^{2}-b^{2} & 2 a b & -2 b \\ 2 a b & 1-a^{2}+b^{2} & 2 a \\ 2 b & -2 a & 1-a^{2}-b^{2}\end{array}\right|=\left(1+a^{2}+b^{2}\right)^{3}$
By using properties of determinants, show that:
$\left|\begin{array}{ccc}1+a^{2}-b^{2} & 2 a b & -2 b \\ 2 a b & 1-a^{2}+b^{2} & 2 a \\ 2 b & -2 a & 1-a^{2}-b^{2}\end{array}\right|=\left(1+a^{2}+b^{2}\right)^{3}$