TRUE/FALSE. if the matrix of coefficients of a homogeneous system of n linear equations in n unknowns has an inverse, then the system does not have infinitely many solutions.

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sammimoose1945 sammimoose1945

05-12-2022
Mathematics

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TRUE/FALSE. if the matrix of coefficients of a homogeneous system of n linear equations in n unknowns has an inverse, then the system does not have infinitely many solutions.

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BhawnaKumari BhawnaKumari · Answer 1 · 2022-12-11T05:27:10-05:00

The given statement is true.

How it is true ?

Because if the matrix of coefficients of a homogenous system of n linear equations is non-singular then there will be the inverse for that matrix.

We know ,

If matrix is non-singular then it has unique solution

and if it singular then it has either no-solution or infinite solution.

So, the above statement is always true.

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