Answer:
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Answer:
A), B) and D) are true
Step-by-step explanation:
A) We can prove it as follows:

B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that
. Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then
.
C) Consider
. This set is orthogonal because
, but S is not orthonormal because the norm of (0,2) is 2≠1.
D) Let A be an orthogonal matrix in
. Then the columns of A form an orthonormal set. We have that
. To see this, note than the component
of the product
is the dot product of the i-th row of
and the jth row of
. But the i-th row of
is equal to the i-th column of
. If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then
E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.
In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set
and suppose that there are coefficients a_i such that
. For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then
then
.
Answer:
Slope = 2 Y-Intercept = (0, 3)
Step-by-step explanation:
Slope :
which is
from two points: point1 (x1 , y1) and point2 (x2, y2).
For the purpose of getting the slope I will be using point (0, 3) as point 1
and point (-3, -3) as point 2.
If you plug in 0 as x1, 3 as y2, -3 for x2, and -3 for y2:
=
= 2
Y-Intercept: The y intercept is the point where the line is touching the y axis. Which in this graph, there is only point (0,3).
Answer:
The first submarine needs to travel at a rate of [-180 – (-1,320)] ÷ 60 = 19 feet per minute.
The second submarine needs to travel at a rate of [-180 – (-1,440)] ÷ 60 = 21 feet per minute.
21 – 19 = 2, so the second submarine must travel 2 feet per minute faster than the first sub.
You dont have a picture so idk the answer but its most likely E if thats an answer choice.