Solve following series of equations ( n + 2 equations n + 2 variables): k 0 q 0 + λ q 0 + c 0 = 0 , k 1 q 1 + λ q 1 + c 1 = 0 , k n q n + λ q n + c n = 0 , q 1 + q 2 + . . . . + q n = 1.The variables are q 0 , q 1 , . . . . . , q n and λ. Note that k and c are series of constants.

Question

Solve following series of equations (  n  +  2 equations   n  +  2 variables):      k    0        q    0    +  λ      q    0    +      c    0    =  0  ,        k    1        q    1    +  λ      q    1    +      c    1    =  0  ,        k    n        q    n    +  λ      q    n    +      c    n    =  0  ,        q    1    +      q    2    +  .  .  .  .  +      q    n    =  1.The variables are       q    0    ,      q    1    ,  .  .  .  .  .  ,      q    n   and   λ. Note that   k and   c are series of constants.

Michaela Alvarado · Accepted Answer

q      i        =                  −                  c          i                                      k          i                +        λ            Substituting in the last equation gives us            ∑              i        =        1                n                      −                  c          i                                      k          i                +        λ              =    1  which can be made into a polynomial equation in       λ  , which you should be able to solve by standard numerical methods.Once you find a root of the above polynomial, substituting       λ   with the value of the root in             q      i        =                  −                  c          i                                      k          i                +        λ             will give the other variables.

Solve following series of equations ( n + 2 equations n + 2 variables): k

Answered question

Answer & Explanation

New Questions in Algebra I