InterviewSolution
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InterviewSolution
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Consider the system of equations `x+y+z=6` `x+2y+3z=10` `x+2y+lambdaz =mu` the system has unique solution ifA. `lambda ne 3`B. `lambda =3, mu =10`C. `lambda =3 , mu ne 10`D. none of these |
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Answer» Correct Answer - A `Delta = |{:(1,,1,,1),(1,,2,,3),(1,,2,,lambda):}|=2lambda +3+2 -2-lambda -6=lambda -3` `Delta_(1) = |{:(6,,1,,1),(10,,2,,3),(mu,,2,,lambda):}|=12lambda +3mu +20 -2mu -10lambda -36` `=2lambda +mu -16` `Delta_(2) =|{:(1,,6,,1),(1,,10,,3),(1,,mu,,lambda):}|=10lambda +18 +mu -10 -3mu -6lambda =4lambda -2mu +8` `Delta_(3) = |{:(1,,1,,6),(1,,2,,10),(1,,2,,mu):}|=2mu +10 +12 -12 -mu -20 =mu -10` Thus the system has unique solutions if `Delta ne 0 " or " lambda ne 3` and the system has infinite solution if `Delta=Delta_(1) =Delta_(2) =Delta_(3) =0 " ot " lambda =3` and `mu=10`. System has no solution if `Delta =0` and at least one of `Delta_(1) ,Delta_(2) ,Delta_(3)` is nonzero of `lambda =3 " and " mu ne =10` |
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