Existence of unique solution of system of equations, x+y+z=β , 5x-y+α z=10 , 2x+3y-z=6 depen

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3 and 4 .Determinants and Matrices

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The existence of unique solution of the system of equations, $x+y+z=\beta $ , $5x-y+\alpha z=10$ , $2x+3y-z=6$ depends on

A

$\alpha $ only

B

$\beta $ only

C

$\alpha $ and $\beta $ both

D

neither $\alpha $ nor $\beta $

Solution

Here, $\Delta \ne 0$

As, $\Delta = \left( {23 – \alpha } \right) \ne 0$

Standard 12

Mathematics

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