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Dennis_Churaev [7]
2 years ago
8

Suppose the system below is consistent for all possible values of f and g. What can you say about the coefficients c and d? Just

ify your answer. x1 + 3x2 = f cx1 + dx2 = g
Mathematics
1 answer:
morpeh [17]2 years ago
7 0

Answer:

The answer is "d \neq 3c,f and g are arbitrary".

Step-by-step explanation:

The matrix of the device is increased  

\left[\begin{array}{ccc}1&3&f\\ c&d&g\\ \end{array}\right]

Reduce the echelon row matrix  

\left[\begin{array}{ccc}1&3&f\\ c&d&g\\ \end{array}\right] \\\\R_1 \leftrightarrow  R_2 \\\\\frac{R_2 -1}{C R_1 \to R_2}   \sim   \left[\begin{array}{ccc} c&d&g\\ 0 & \frac{3c-d}{c}& \frac{cf-g}{c}\\ \end{array}\right]

Therefore, if 3c\neq 0 is d \neq  3c, the device is valid.  Therefore d \neq are arbitrary 3c, g and f.

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