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QuestionFind values of h for which the matrix is consistent: [12−45h−20] \left[\begin{array}{rrr} 1 & 2 & -4 \\ 5 & h & -20 \end{array}\right] Choose A, B, C, or D.

Studdy Solution

STEP 1

Assumptions1. The given matrix is an augmented matrix of a linear system. . The system is consistent if there is at least one solution.
3. The system is inconsistent if there is no solution.
4. The system is consistent if the ratio of the coefficients of the variables in the equations represented by the matrix are equal.

STEP 2

The given matrix represents the system of linear equationsx+2y=−45x+hy=−20\begin{align*} x +2y &= -4 \\ 5x + hy &= -20\end{align*}

STEP 3

For the system to be consistent, the ratios of the coefficients of xx and yy in both equations should be equal. This means15=2h\frac{1}{5} = \frac{2}{h}

STEP 4

olve the above equation for hh.
h=×21h = \frac{ \times2}{1}

STEP 5

Calculate the value of hh.
h=101=10h = \frac{10}{1} =10The matrix is the augmented matrix of a consistent linear system if h=10h =10.

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