If-x-y-z-are-in-AP-Then-the-value-of-the-determinant-determinant-a-2-a-3-a-2x-a-3-a-4-a-2y-a-4-a-5-a-2z-is-

Question Number 55846 by gunawan last updated on 05/Mar/19

If x, y, z are in AP . Then the value of the

determinant

| \begin{matrix} a + 2 & a + 3 & a + 2 x \\ a + 3 & a + 4 & a + 2 y \\ a + 4 & a + 5 & a + 2 z \end{matrix} | is

Answered by math1967 last updated on 05/Mar/19

| \begin{matrix} a + 2 & a + 3 & a + 2 x \\ a + 3 - a - 2 & a + 4 - a - 3 & a + 2 y - a - 2 x \\ a + 4 - a - 3 & a + 5 - a - 4 & a + 2 z - a - 2 y \end{matrix} | R_{2}^{^{'}} \to R_{2} - R_{1}, R_{3}^{^{'}} \to R_{3} - R_{2}

| \begin{matrix} a + 2 & a + 3 & a + 2 x \\ 1 & 1 & 2 (y - x) \\ 1 & 1 & 2 (z - y) \end{matrix} |

| \begin{matrix} a + 2 & a + 3 & a + 2 x \\ 1 & 1 & 2 (y - x) \\ 1 & 1 & 2 (y - x) \end{matrix} | ∵ x, y, z are inA . P ∴ y - x = z - y

= 0 ans [R_{2} and R_{3} identical]

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