An ordered pair α ,   β for which the system of linear equations 1 + α x + β y + z = 2 α x + 1 + β y + z = 3 α x + β y + 2 z = 2 has a unique solution, is :

Question

An ordered pair &#945; , &#160; &#946; for which the system of linear equations 1 + &#945; x + &#946; y + z = 2 &#945; x + 1 + &#946; y + z = 3 &#945; x + &#946; y + 2 z = 2 has a unique solution, is :

Aicharya · Accepted Answer

For unique solution 1 + &#945; &#946; 1 &#945; 1 + &#946; 1 &#945; &#946; 2 &#8800; 0 Applying C 1 &#8594; C 1 + C 2 + C 3 , we get &#945; + &#946; + 2 &#946; 1 &#945; + &#946; + 2 1 + &#946; 1 &#945; + &#946; + 2 &#946; 2 &#8800; 0 &#8658; &#945; + &#946; + 2 1 &#946; 1 1 1 + &#946; 1 1 &#946; 2 &#8800; 0 &#8658; &#945; + &#946; + 2 &#8800; 0 Clearly, point 2 , &#160; 4 satisfying the given condition.

An ordered pair α ,   β for which the system of linear equations 1 + α x + β y + z…

Solution

An ordered pair &#945; , &#160; &#946; for which the system of linear equations 1 + &#945; x + &#946; y + z…

Solution

An ordered pair α , β for which the system of linear equations 1 + α x + β y + z…