Question

$\left| \begin{matrix} a & a + b & a + 2b \\ a + 2b & a & a + b \\ a + b & a + 2b & a \end{matrix} \right|$ = mbⁿ(a + b) Then :

• A. m = 9, n = 1
• B. m = 1, n = 2
• C. m = 9, n = 2
• D. None

Answer 1

Answer: (C)

m = 9, n = 2

Answer 2

∆= $\left| \begin{matrix} a & a + b & a + 2b \\ a + 2b & a & a + b \\ a + b & a + 2b & a \end{matrix} \right|$

= 3(a + b) $\left| \begin{matrix} 1 & a + b & a + 2b \\ 1 & a & a + b \\ 1 & a + 2b & a \end{matrix} \right|$ C₁→C₁+C₂+ C₃

= 3(a + b) $\left| \begin{matrix} 1 & a + b & a + 2b \\ 0 & –b & –b \\ 0 & b & –2b \end{matrix} \right|$

= 9b² (a + b)

= mbⁿ (a + b)

∴ m = 9, n = 2