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8 August, 12:38

A) For what value (s) of k is the following SoLE inconsistent?

x - 2y + 4z = 3

4x + 5y + kz = 9

y + 3z = 2

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Answers (1)
  1. 8 August, 14:39
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    Answer: z = 55.

    Step-by-step explanation:

    we want to find values of k that make this inconsistent.

    x - 2y + 4z = 3

    4x + 5y + kz = 9

    y + 3z = 2

    First, can you can see that k never can make some of the equations linearly dependent because of how constructed is the set. Now, let's see if there are values of k that give problems to our system.

    To see it, let's solve the system.

    from the third equation we can write y = 2 - 3z, and we can replace it into the first two equations:

    x - 2 (2 - 3z) + 4z = 3

    4x + 5 (2 - 3z) + kz = 9

    simplify both equations and get

    x + 10z = 7

    4x + (k - 15) * z = - 1

    from the first equation, we have that:

    x = 7 - 10z

    we can replace it into the other equation:

    4 * (7 - 10z) + (k - 15) * z = - 1

    28 - 40z + (k - 15) * z = - 1

    (k - 55) * z = - 29

    z = - 29 / (k - 55)

    here you can see that the only value of z that has problems is z = 55, because we never can have a 0 in the denominator.
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