Does the following system have a unique solution? why?
a) no, because the determinant of the coefficient matrix is 0.
b) no, because the determinant of the coefficient matrix is 12.
c) yes, because the determinant of the coefficient matrix is 0.
d) yes, because the determinant of the coefficient matrix is 12.

A) No, because the determinant of the coefficient matrix is 0.

Step-by-step explanation:

The determinant of the matrix   is .

The given system is .

The coefficient matrix for this system is:

The determinant of this matrix is

Since the determinant is zero, the system has no unique solution.

The correct choice is A.

A) No, because the determinant of the coefficient matrix is 0.  

Step-by-step explanation:

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

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).