Question

If A = ${\displaystyle \left[\begin{array}{ccc}1& 1& 0\\ 2& 1& 5\\ 1& 2& 1\end{array}\right]}$, then a₁₁A₂₁ + a₁₂A₂₂ + a₁₃A₂₃ is equal to ______.

Options

• 1

• 0

• –1

• 2

Answer 1

If A = ${\displaystyle \left[\begin{array}{ccc}1& 1& 0\\ 2& 1& 5\\ 1& 2& 1\end{array}\right]}$, then a₁₁A₂₁ + a₁₂A₂₂ + a₁₃A₂₃ is equal to 0.

Explanation:

Given, A = ${\displaystyle \left[\begin{array}{ccc}1& 1& 0\\ 2& 1& 5\\ 1& 2& 1\end{array}\right]}$

Since, the sum of the product of element other than the corresponding cofactor is zero.

∴ a₁₁A₂₁ + a₁₂A₂₂ + a₁₃A₂₃ = 0