1-2-3-3-4-5-5-6-7-find-determinant-of-given-matrix-

Question Number 41305 by sameer12 last updated on 05/Aug/18

[\begin{matrix} 1 & 2 & 3 \\ 3 & 4 & 5 \\ 5 & 6 & 7 \end{matrix}]

f i n d d e t e r m i n a n t o f g i v e n m a t r i x ?

Commented by MrW3 last updated on 05/Aug/18

r o w 3 - r o w 2 :

[\begin{matrix} 1 & 2 & 3 \\ 3 & 4 & 5 \\ 2 & 2 & 2 \end{matrix}]

r o w 2 - r o w 1 :

[\begin{matrix} 1 & 2 & 3 \\ 1 & 1 & 1 \\ 2 & 2 & 2 \end{matrix}]

r o w 3 - 2 \times r o w 2 :

[\begin{matrix} 1 & 2 & 3 \\ 1 & 1 & 1 \\ 0 & 0 & 0 \end{matrix}]

\Rightarrow d e t e r m i n a n t = 0

Answered by malwaan last updated on 05/Aug/18

(1 \times 4 \times 7 + 2 \times 5 \times 5 + 3 \times 3 \times 6) -

(3 \times 4 \times 5 + 2 \times 3 \times 7 + 5 \times 6 \times 1)

= (28 + 50 + 54) - (60 + 42 + 30)

= 132 - 132 = 0

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