The span of 3 vectors can have dimension at most 3, so 9 is certainly not correct.
Check whether the 3 vectors are linearly independent. If they are not, then there is some choice of scalars 
(not all zero) such that
which leads to the system of linear equations,
From the third equation, we have 
, and substituting this into the second equation gives
and in turn, 
. Substituting these into the first equation gives
which tells us that any value of 
will work. If 
, then 
and 
. Therefore the 3 vectors are not linearly independent, so their span cannot have dimension 3.
Repeating the calculations above while taking only 2 of the given vectors at a time, we see that they are pairwise linearly independent, so the span of each pair has dimension 2. This means the span of all 3 vectors taken at once must be 2.
Answer:
0,2 0r 2/2
Step-by-step explanation:
Slope Formula: y2 - y1 / x2 - x1
(m and slope represent the same quantity)
m = 1 - - 5 / -4 - 0
m = 1 + 5 / -4
m = 6 / -4
m = -3/2
Now that we know the slope, we can plug the slope and one of our points into slope-intercept form (y = mx + b) and solve for b. I will be using the point (-4,1).
y = -3/2x + b
1 = -3/2(-4) + b
1 = 6 + b
b = -5
In point form, the y-intercept is (0, -5).
Therefore, to get the equation all we need to do is plug in our slope and b-value to slope-intercept form.
Equation: y = -3/2 x - 5
To check the point (-6, -14) we plug it into our equation and see if the two sides are equal.
-14 = -3/2(-6) - 5
-14 = 9 - 5
-14 = 4
-14 does not equal 4, therefore the point is NOT on the line.
Hope this helps!
Answer:
Exact fraction form: 1/2 Decimal form: 0.5
