With

we have

so
has one eigenvalue,
, with multiplicity 3.
In order for
to not be defective, we need the dimension of the eigenspace to match the multiplicity of the repeated eigenvalue 2. But
has nullspace of dimension 2, since

That is, we can only obtain 2 eigenvectors,

and there is no other. We needed 3 in order to complete the basis of eigenvectors.
In order to get your answer, take the number of text messages you send each day (12) and subtract it from the number you and your sister send (26). When you get the answer from subtracting both of these numbers, take the answer from your subtraction and add it to the number of text messages that you send a day (12).
Answer:
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Answer (<u>assuming it can be written in slope-intercept form)</u>:

Step-by-step explanation:
1) First, find the slope of the line. Use the slope formula,
. Substitute the x and y values of the given points into the formula and solve:
So, the slope is
.
2) Now, use the point-slope formula
to write the equation of the line. Substitute
,
, and
for real values.
Since
represents the slope, substitute
for it. Since
and
represent the x and y values of one point the line intersects, choose from any one of the given points (it doesn't matter which one, either way the result equals the same thing) and substitute its x and y values into the formula as well. (I chose (4,5), as seen below.) From there, isolate y to place the equation in slope-intercept form (
format) and find the following answer: