Question

Matrix A = ${\displaystyle \left[\begin{array}{ccc}1& 2& 3\\ 1& 1& 5\\ 2& 4& 7\end{array}\right]}$ then the value of a₃₁ A₃₁ + a₃₂ A₃₂ + a₃₃ A₃₃ is ______.

विकल्प

• 1

• 13

• –1

• –13

Answer 1

Matrix A = ${\displaystyle \left[\begin{array}{ccc}1& 2& 3\\ 1& 1& 5\\ 2& 4& 7\end{array}\right]}$ then the value of a₃₁ A₃₁ + a₃₂ A₃₂ + a₃₃ A₃₃ is –1.

Explanation:

Here A = ${\displaystyle \left[\begin{array}{ccc}1& 2& 3\\ 1& 1& 5\\ 2& 4& 7\end{array}\right]}$ 

we know that,

a₃₁ A₃₁ + a₃₂ A₃₂ + a₃₃ A₃₃ = |A|

= +1(7 – 20) – 2(7 – 10) + 3(4 – 2)

= – 13 + 6 + 6

= – 1