1.

whichof the following is//aretrue for Delta= |{:(a^(2),,1,,a+c),(0,,b^(2)+1,,b+c),(0,,b+c,,c^(2)+1):}| ?

Answer»

`Delta ge 0` for realvaluesof a,b,c
`Delta LE 0` for realvalues of a,b,c
`Delta =|{:(bc-1,,0,,0),(1,,ac,,-a),(-b,,-a,,ab):}|`
`Delta =0` IFBC =1where a,b,CARE non-zero

Solution :`|{:(a^(2),,1,,a+c),(0,,b^(2)+1,,b+c),(0,,b+c,,c^(1)+1):}|=|{:(a,,0,,1),(0,,b,,1),(0,,1,,c):}||{:(a,,0,,1),(0,,b,,1),(0,,1,,c):}|`
`=|{:(a,,0,,1),(0,,b,,1),(0,,1,,c):}|^(2)`
`=(abc -a)^(2)= a^(2) (bc-1)^(2)`
`=|{:(bc-1,,0,,0),(1,,ac,,-a),(-b,,-a,,ab):}|`
{Determinant formed bycofactors)


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