If x, y, z are in arithmetic progression with common difference d, x
e 3d, and the determinant of the matrix \left[ {\begin{matrix} 3 & {4\sqrt 2 } & x \ 4 & {5\sqrt 2 } & y \ 5 & k & z \ \end{matrix} } ight] is zero, then the value of k2 is :

Question

If x, y, z are in arithmetic progression with common difference d, x 
e 3d, and the determinant of the matrix \left[ {\begin{matrix} 3 & {4\sqrt 2 } & x \ 4 & {5\sqrt 2 } & y \ 5 & k & z \ \end{matrix} } ight] is zero, then the value of k2 is :

Accepted Answer

Answer: A. 72 \left| {\begin{matrix} 3 & {4\sqrt 2 } & x \ 4 & {5\sqrt 2 } & y \ 5 & k & z \ \end{matrix} } ight| = 0 {R_1} 	o {R_1} + {R_3} - 2{R_2} \Rightarrow \left| {\begin{matrix} 0 & {4\sqrt 2 - k - 10\sqrt 2 } & 0 \ 4 & {5\sqrt 2 } & y \ 5 & k & z \ \end{matrix} } ight| = 0 { \because 2y = x + z} \Rightarrow (k - 6\sqrt 2 )(4z - 5y) = 0 \Rightarrow k = 6\sqrt 2 or 4z = 5y (Not possible \because x, y, z in A.P.) So, k2 = 72 	herefore Option (A)

If x, y, z are in arithmetic progression with common difference d, x $$\ne$$ 3d, and the determinant of the matrix $$\left[ {\begin{matrix} 3 & {4\sqrt 2 } & x \\ 4 & {5\sqrt 2 } & y \\ 5 & k & z \\ \end{matrix} } \right]$$ is zero, then the value of k2 is :

Answer

Explanation

More JEE Math questions