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:
$15 < $4n + $5
Step-by-step explanation:
We know that Billy needs to make more than $15 between his allowance and the lawns that he mows. This means our inequality should include $15<. Also, since Billy will make $4 per lawn, that means we need to multiply $4 by the number of lawns he needs to mow, n: $4n. So far we have the following: $15<$4n. Next, we know that he makes $5 each week, on top of what he makes mowing each law. This means we need to add the $5 to the $4n. When we put all of these pieces together, we will get the following inequality: $15<$4n+$5
Answer: 
Step-by-step explanation:
You can observe in the figure that JK is a tangent and KH is a secant and both intersect at the point K. Then, according to the Intersecting secant-tangent Theorem:

You know that:

Then KE is:



Now you can substitute the value of KE and the value of KH into
and solve for JK. Then the result is:
Jenna has $43 and Heidi has $17.
Step-by-step explanation:
Total amount = $60
Let,
Amount of Jenna = x
Amount of Heidi = y
According to given statement;
x+y=60 Eqn 1
x=2y+9 Eqn 2
Putting value of Eqn 2 in Eqn 1;

Dividing both sides by 3,

Putting y=17 in Eqn 2

Jenna has $43 and Heidi has $17.
Keywords: linear equations, substitution method
Learn more about substitution method at:
#LearnwithBrainly