Answer: The answer is (4, 600)
Step-by-step explanation:
Answer:
![\\ \gamma= \frac{a\cdot b}{b\cdot b}](https://tex.z-dn.net/?f=%5C%5C%20%5Cgamma%3D%20%5Cfrac%7Ba%5Ccdot%20b%7D%7Bb%5Ccdot%20b%7D)
Step-by-step explanation:
The question to be solved is the following :
Suppose that a and b are any n-vectors. Show that we can always find a scalar γ so that (a − γb) ⊥ b, and that γ is unique if
. Recall that given two vectors a,b a⊥ b if and only if
where
is the dot product defined in
. Suposse that
. We want to find γ such that
. Given that the dot product can be distributed and that it is linear, the following equation is obtained
![(a-\gamma b)\cdot b = 0 = a\cdot b - (\gamma b)\cdot b= a\cdot b - \gamma b\cdot b](https://tex.z-dn.net/?f=%28a-%5Cgamma%20b%29%5Ccdot%20b%20%3D%200%20%3D%20a%5Ccdot%20b%20-%20%28%5Cgamma%20b%29%5Ccdot%20b%3D%20a%5Ccdot%20b%20-%20%5Cgamma%20b%5Ccdot%20b)
Recall that
are both real numbers, so by solving the value of γ, we get that
![\gamma= \frac{a\cdot b}{b\cdot b}](https://tex.z-dn.net/?f=%5Cgamma%3D%20%5Cfrac%7Ba%5Ccdot%20b%7D%7Bb%5Ccdot%20b%7D)
By construction, this γ is unique if
, since if there was a
such that
, then
![\gamma_2 = \frac{a\cdot b}{b\cdot b}= \gamma](https://tex.z-dn.net/?f=%5Cgamma_2%20%3D%20%5Cfrac%7Ba%5Ccdot%20b%7D%7Bb%5Ccdot%20b%7D%3D%20%5Cgamma)
The correct answer for this question is this one: "B. increase your scale values"
<span>When creating a scatterplot, if the points are too close together to see the relationship, You adjust your graph by </span><em>increasing your scale values</em>
Hope this helps answer your question and have a nice day ahead.
-3 on a number line would look like 3 right from 0.
Let's just say we have a number line. A number line is a line that represents numbers. I'll say the positive side is on the top/left and the negative side (-3) on the bottom/right. -3 is a negative number. There is the sign (-) before 3. That indicates it's a negative number. Since it's a negative and 3, we move 3 down or right.