Given:
![\[2x~-~5y\text{ }+\text{ }3\text{ }=\text{ }0\text{ }\ldots \text{ }\left( 1 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-844b4efc0093e95bbc2b0d694ed898f4_l3.png "Rendered by QuickLaTeX.com")
![\[5x~-~9y\text{ }+~\lambda ~=\text{ }0\text{ }\ldots \text{ }\left( 2 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-22012fad57145ade90109106094d76d7_l3.png "Rendered by QuickLaTeX.com")
And ,
![\[x~-~2y\text{ }+\text{ }1\text{ }=\text{ }0\text{ }\ldots \text{ }\left( 3 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b5f0d28637eab6d753ffc66f7875bbb5_l3.png "Rendered by QuickLaTeX.com")
It is given that the three lines are concurrent.
Now, consider the following determinant:
![\[2\left( -9\text{ }+\text{ }2\lambda \right)\text{ }+\text{ }5\left( 5\text{ }~\lambda \right)\text{ }+\text{ }3\left( -10\text{ }+\text{ }9 \right)\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7f8deeded9ca8cd0b4233eefdbfc1fc7_l3.png "Rendered by QuickLaTeX.com")
![\[-18\text{ }+\text{ }4\lambda ~+\text{ }25\text{ }\text{ }5\lambda ~\text{ }3\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8a81770da9989d379a31c93d320ed912_l3.png "Rendered by QuickLaTeX.com")
![\[\lambda ~=\text{ }4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3d8cb960f4a3e0a884ab913467561e30_l3.png "Rendered by QuickLaTeX.com")
∴ The value of λ is 4.
Given:
And ,
It is given that the three lines are concurrent.
Now, consider the following determinant:
∴ The value of λ is 4.