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 negative 15 2nd Column 21 3rd Column h 2nd Row 1st Column 5 2nd Column negative 7 3rd Column negative 3 EndMatrix ]

Answer 1

Answer: h = 9

Step-by-step explanation: A system of linear equations is consistent when it has at least one solution.

The matrix given is:

$\left[\begin{array}{ccc}-15&21&h\\5&-7&-3\end{array}\right]$

Transform this matrix in a row-echelon form:

$\left[\begin{array}{ccc}-15&21&h\\5&-7&-3\end{array}\right]$   $R_{2} = 3R_{2}+R_{1}$ $\left[\begin{array}{ccc}-15&21&h\\0&0&-9+h\end{array}\right]$

For this row-echelon form to have solutions:

-9 + h = 0

h = 9

For this system to be consistent: h = 9.