Question

If $\left| \begin{matrix} a & a + b & a + 2b \\ a + 2b & a & a + b \\ a + b & a + 2b & a \end{matrix} \right|$= mbⁿ (a + b), then

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

Answer 1

Answer: (C)

m = 9, n = 2

Answer 2

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)

\ m = 9, n = 2