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Equivalent Sets

Let =f g ha...

Question

Let $△ = ∣ ∣ ∣ ∣ \begin{matrix} f & g & h a & b & c x & y & z \end{matrix} ∣ ∣ ∣ ∣,$ then which of the following statement(s) is(are) correct?
(where $M_{i j}$ is minor of element $a_{i j}$ )

A

x M_{31} - y M_{32} + z M_{33} = 0

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B

x M_{31} - y M_{32} + z M_{33} = △

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C

- g M_{12} + b M_{22} - y M_{32} = △

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D

- g M_{12} + b M_{22} + y M_{32} = 0

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Solution

The correct option is C $- g M_{12} + b M_{22} - y M_{32} = △$
Guven : $△ = ∣ ∣ ∣ ∣ \begin{matrix} f & g & h a & b & c x & y & z \end{matrix} ∣ ∣ ∣ ∣$
we know, $△$ = sum of product of elements in any row/column to its corresponding co-factors.
Expanding along $R_{3} : △ = x M_{31} - y M_{32} + z M_{33}$
expanding along $C_{2} : △ = - g M_{12} + b M_{22} - y M_{32}$

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Equivalent Sets

Standard VI Mathematics

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