Determine the value(s) of h such that the matrix is the augmented matrix of a co

Question

Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. 1 h 2 -5 20 -12 Select the correct choice below and, f necessary, ill inthe answer box to complete your choice O A. The matrix is the augmented matrix of a consistent linear system if h # O B. The matrix is the augmented matrix of a consistent linear system if h = O C. The matrix is the augmented matrix of a consistent linear system for every value of h. (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) (Use a comma to separate answers as needed. lype an integer or a simplified fraction.) O D. The matrix is not the augmented matrix of a consistent linear system for any value of h

Explanation / Answer

Consistent system would be if the system has no solutions

Note that

1*(-5)=-5

2*(-6)=-12

So if we choose h so that

h*(-5)=20 ie h=-4

Then coefficients of the variables ,which is the first two columns, are multiples of each other

Then we have no solution as we would then have two distince parallel lines

Hence system is consisten for : h not equal to -4

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