# Linear system of equations

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A little hint will also suffice

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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.

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My solution:- Since the Determinant of matrix is Zero. So it will posses non trivial solution. Now what should be the answer ? According to me Option D as rank is < Order so infinite number of solutions
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Test the consistency of the following system of equations and solve if possible $3x + 3y +2z = 1$ $x + 2y = 4$ $10y + 3z = -2$ $2x - 3y -z = 5$