A) For what value(s) of k is the following SoLE inconsistent? x - 2y + 4z = 3
4x + 5y + kz = 9
y + 3z = 2

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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step-by-step explanation:

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168

step-by-step explanation:

i am pretty sure that the answer is 168