Question

Determine the​ value(s) of h such that the matrix is the augmented matrix of a consistent linear system. [Start 2 By 3 Matrix 1st Row 1st Column 1 2nd Column 4 3rd Column negative 2 2nd Row 1st Column 3 2nd Column h 3rd Column negative 6 EndMatrix ]

Answer 1

Explanation:

Consider the augments matrix (the right most column is the extra vector).

`\left[\begin{matrix} 1 & 4 & -2 \\3 & h & -6\end{matrix}\right]`

By multypling the first row by 3 and substracting it from the second row and saving the result in the second row we get the matrix

`\left[\begin{matrix} 1 & 4 & -2 \\0 & h-12 & 0\end{matrix}\right]`

Note that since the value of the third column in the second row is 0, any value of h gives us a consistent system. An inconsistent system is when we get a row of zeros that is equal to a number different from 0.