Determing the values of h such that the matrix is the augmented matrix of a cons

Question

Determing the values of h such that the matrix is the augmented matrix of a consistent linear syste

Select the correct choice below and, if necessary, fill in the answer box to complete your choice

A) Matrix is an augmented matrix of a consistant linear system if h= ?

B) Matrix is an augmented matrix of a consistant linear system if h doesnt equal ?

C) The matrix is an augmented matrix of a consistant linear system for every value of h

D) The matrix is not the augmented matrix of a consistant linear system for any value of h

Explanation / Answer

This is the intersection of two lines, so to be consistent the slopes must be different,

-1/5 and h/10 must not be the same , h doesn't equal to -2

ie the determinant of the coefficient matrix cannot be 0

But in this case, since the slope of first and third doesn't match with each other hence the correct answer is option B

B) Matrix is an augmented matrix of a consistant linear system if h doesnt equal = -2

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