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  • Provide solution for RD Sharma maths class 12 chapter Determinants exercise 5.3 question 3

Provide solution for RD Sharma maths class 12 chapter Determinants exercise 5.3 question 3

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Answer: Proved.

Hints: First find determinant and the value of a and b, to prove the given equation.

\mathbf{Given\! :}\left ( a,0 \right )\! , \left ( 0,b \right )\: and\: \left ( 1,1 \right ) are\; collinear.

Explanation: Determinant=0

\Rightarrow \begin{vmatrix} a &0 &1 \\ 0 &b &1 \\ 1 &1 &1 \end{vmatrix}=0

\Rightarrow a\! \begin{vmatrix} b &1 \\ 1 &1 \end{vmatrix}-0\! \begin{vmatrix} 0 &1 \\ 1 &1 \end{vmatrix}+1\! \begin{vmatrix} 0 &b \\ 1 &1 \end{vmatrix}=0

\Rightarrow a\! \left ( b-1 \right )-0 +1\! \left ( 0-b \right )=0

\Rightarrow ab-a-b=0

\Rightarrow ab=a+b

\Rightarrow a+b=ab

Hence, proved the given equation.

Posted by

Gurleen Kaur

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