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

$$\left[\begin{array}{ccc}1& 2& 3\\ 3& 4& 5\\ 5& 6& 7\end{array}\right]$$$$finddeterminantofgivenmatrix?$$

Commented by MrW3 last updated on 05/Aug/18

$$row3-row2:$$$$\left[\begin{array}{ccc}1& 2& 3\\ 3& 4& 5\\ 2& 2& 2\end{array}\right]$$$$row2-row1:$$$$\left[\begin{array}{ccc}1& 2& 3\\ 1& 1& 1\\ 2& 2& 2\end{array}\right]$$$$row3-2\times row2:$$$$\left[\begin{array}{ccc}1& 2& 3\\ 1& 1& 1\\ 0& 0& 0\end{array}\right]$$$$\Rightarrow determinant=0$$

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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