Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions. x + 2y – 3z = 4 3x – y + 5z = 2 4x + y +(a– 14)z = a +2

The system has solution when:

The system has no solution when:

Step-by-step explanation:

First rewrite the system in its augmented matrix form

Let´s apply row reduction process to  its associated augmented matrix:

Now we have this:

We can conclude now:

The system has no solution when:

And the system has solution when:

correct answer:

b.(19,-2)

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it