Let's go:
The centroid of a triangle is the point of intersection of its medians. The distance from de centroid to some vertex of triangle to which it belongs is equal to 2/3 of the length of its median:
BM = 18/3 = 6
I hope I helped you.
Answer:
True
True
False
Step-by-step explanation:
TRUE
If the equation Ax = 0 has only the trivial solution, then A is row equivalent to the n × n identity matrix
Here's why
If the equation Ax = 0 has only the trivial solution the determinant of the matrix is NOT 0 and the matrix is invertible therefore it is row equivalent to the nxn identity matrix.
TRUE
If the columns of A span ℝ^n , then the columns are linearly independent
Here's why
Remember that the rank nullity theorem states that
![\text{rank}(A) + \text{Nullity}(A) = \text{Dim}(V)](https://tex.z-dn.net/?f=%5Ctext%7Brank%7D%28A%29%20%2B%20%5Ctext%7BNullity%7D%28A%29%20%3D%20%5Ctext%7BDim%7D%28V%29)
According to the information given we know that
![\text{rank}(A) = n \\dim(V) = n \\](https://tex.z-dn.net/?f=%5Ctext%7Brank%7D%28A%29%20%3D%20n%20%5C%5Cdim%28V%29%20%3D%20n%20%5C%5C)
Therefore you have
![n + \text{Nullity}(A) = n](https://tex.z-dn.net/?f=n%20%2B%20%5Ctext%7BNullity%7D%28A%29%20%3D%20n)
and
![\text{Nullity}(A) = 0](https://tex.z-dn.net/?f=%5Ctext%7BNullity%7D%28A%29%20%3D%200)
Which is equivalent to the problem we just solved.
FALSE
If A is an n × n matrix, then the equation Ax = b has at least one solution for each b in ℝ^n
Here's why
Take b as a non null vector and A=0, then Ax = 0 and Ax=b will have no solution.
Hello there!
The point (2,-3) would lay in quadrant IV, or 4.
Basically:
Points that are (x, y) or positive x and positive y ay in quadrant 1, or I.
Points that are (-x, y) or negative x and positive y lay in quadrant 2, or II.
Points that are (-x, -y) or negative x and negative y usually lay in quadrant 3, or III.
Points that are (x, -y) or positive x and negative y usually lay in quadrant 4, or IV.
I hope this was helpful! Have a great rest of your day :)
Not sure but i think is -4.666..
We're literally just comparing 200 to 800 here.
800 is 4× bigger than 200, of course.
To put that in a percent...
Well, 1 = 100%. (it's a whole)
So 4 = 400%