Linear system of equations

Question

 

Comments

A little hint will also suffice

Answer 1

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Comments

Sir in unique solution case if lambda and micro aren't equal to 5 and 9 then the rank of both will be 3 right ?

Sir when we calculate rank and say I reduce the matrix to upper triangular matrix then the rank will always be n ?

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 For a unique solution case, if $\lambda\neq5 $, is enough, it does not depend on the $\mu.$

for this case $\mu=9$ or $\mu\neq9$ it doesn't matter in case of a unique solution.Because when $\lambda\neq5$,rank of (A)=3 and rank(A:B) is also $3$.

Rank=Maximum Number of independent Rows/Columns.

Rank=Dimension(Order)-Nullity.