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

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

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