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Suppose the system below is consistent for all possible values of f and g. What can you say about the coefficients c and d? Justify your answer. x1 + 3x2 = f cx1 + dx2 = g

Sagot :

Answer:

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

Step-by-step explanation:

The matrix of the device is increased  

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

Reduce the echelon row matrix  

[tex]\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][/tex]

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

MrRoyal

The values of the coefficients c and d are 1 and 3, respectively

The system of equations are given as:

[tex]x_1 + 3x_2 = f[/tex]

[tex]cx_1 + dx_2 = g[/tex]

From the question, we understand that the system of equations is consistent.

Assume that the system of equations is also dependent, then it means that:

[tex]c =1[/tex]

[tex]d =3[/tex]

[tex]g =f[/tex]

Hence, the values of the coefficients c and d are 1 and 3, respectively

Read more about systems of equations at:

https://brainly.com/question/13729904

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