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Question: If x, y, z are integers in A.P., lying between 1 and 9, and x51, y41 and z31 are three digit number...

If x, y, z are integers in A.P., lying between 1 and 9, and x51,

y41 and z31 are three digit numbers then the value of

∣543x51y41z31xyz∣\left| \begin{matrix} 5 & 4 & 3 \\ x51 & y41 & z31 \\ x & y & z \end{matrix} \right| is

A

x + y + z

B

0

C

x – y + z

D

x – y – z

Answer

0

Explanation

Solution

5 & 4 & 3 \\ 100x + 51 & 100y + 41 & 100y + 31 \\ x & y & z \end{matrix} \right|$$ R<sub>1</sub> → R<sub>2</sub> – (100R<sub>3</sub>) ∆ = $\left| \begin{matrix} 5 & 4 & 3 \\ 51 & 41 & 31 \\ x & y & z \end{matrix} \right|$⇒ ∆ = 0