I am terrible at math please help me.
1 answer:
You might be interested in
Answer:
See the proof below.
Step-by-step explanation:
What we need to proof is this: "Assuming X a vector space over a scalar field C. Let X= {x1,x2,....,xn} a set of vectors in X, where . If the set X is linearly dependent if and only if at least one of the vectors in X can be written as a linear combination of the other vectors"
Proof
Since we have a if and only if w need to proof the statement on the two possible ways.
If X is linearly dependent, then a vector is a linear combination
We suppose the set is linearly dependent, so then by definition we have scalars
in C such that:
And not all the scalars are equal to 0.
Since at least one constant is non zero we can assume for example that , and we have this:
We can divide by c1 since we assume that and we have this:
And as we can see the vector can be written a a linear combination of the remaining vectors
. We select v1 but we can select any vector and we get the same result.
If a vector is a linear combination, then X is linearly dependent
We assume on this case that X is a linear combination of the remaining vectors, as on the last part we can assume that we select and we have this:
For scalars defined in C. So then we have this:
So then we can conclude that the set X is linearly dependent.
And that complet the proof for this case.
Answer:
See below:
Step-by-step explanation:
Hello! I hope you are having a nice day.
We can solve this equation in a single step, we just need a bit of theory and a graph.
We can first see that its in form. Which is also known as Slope-Intercept form.
This means that we know the following.
is the y coordinate of the y intercept.
is the slope of the line.
Since we know that, we can see that from our equation that the slope of the line is 3 and the y intercept is (0,-7).
Now that we've gotten that, we can start graphing.
The y intercept is -7 so we can plot (0,-7) as one of our points.
The slope of 3 means that we got up 3 units then right a single unit.
Therefore, another point could be (1,-4).
With our two points, we can create our graph by creating a straight line through those two points and therefore plotting our line.
Cheers!
