For the system of linear equations 2 x - y + 3 z = 5 3 x + 2 y - z = 7 4 x + 5 y + α z = β , which of the following is NOT correct?

Question

For the system of linear equations 2 x - y + 3 z = 5 3 x + 2 y - z = 7 4 x + 5 y + &#945; z = &#946; , which of the following is NOT correct?

Aicharya · Accepted Answer

Given,
For the system of linear equations
$2 x - y + 3 z = 5$
$3 x + 2 y - z = 7$
$4 x + 5 y + α z = β$ ,
Now finding,
$D = |\begin{matrix} 2 & - 1 & 3 \\ 3 & 2 & - 1 \\ 4 & 5 & α \end{matrix}|$
$\Rightarrow D = 2 (2 α + 5) + (3 α + 4) + 3 (7)$
$\Rightarrow D = 7 α + 35$
Now we know that, for unique solution $D \neq 0 \Rightarrow α \neq - 5$
So, in option $(B)$ $α = - 6$ corresponds to infinitely many solution, which is completely wrong hence, this is answer.

For the system of linear equations 2 x - y + 3 z = 5 3 x + 2 y - z = 7 4 x + 5 y + α z = β , which…

Solution

For the system of linear equations 2 x - y + 3 z = 5 3 x + 2 y - z = 7 4 x + 5 y + &#945; z = &#946; , which…

Solution

For the system of linear equations 2 x - y + 3 z = 5 3 x + 2 y - z = 7 4 x + 5 y + α z = β , which…