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 
.
The computation shows that the time when they'll meet each other will be 175 minutes.
<h3>How to illustrate the information?</h3>
From the information, it takes the first student 25 minutes to complete one lap, and it takes the second student 35 minutes to complete one lap.
It should be noted that the time when they'll meet each other will be the lowest common multiple of 25 and 35.
This will be 175 minutes.
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Answer:
B. 9.6 %.
Step-by-step explanation:
A = P e^rt
His investment doubles so it comes to 3000 * 2 = $6000.
Substituting in the formula>
6000 = 3000e^7.2r ehere r is the interest rate.
e^7.2r = 2
Taking logs
7.2r = ln 2
r = ln2 / 7.2
r = 0.096
So the rate is 9.6%.
Answer:
8,820
Step-by-step explanation:
One candle:
½ × 10 × 7 × 6
= 210 cm³
42 candles:
42 × 210
= 8,820 cm³
