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:
<h2>7.5%</h2>
Step-by-step explanation:
871 miles ........... 13 hours
469 miles ............x hours
x = 469×13/871 = 7 hours
Answer:
Total number of dogs is 5.
Step-by-step explanation:
Cups of food each dog gets=
Here,each dog eats two-third cups of dog food.
Amount of dog food used=
A total of three and one-third cups of food is used up.
Let the number of dogs be x.
To find the number of dogs,divide total dog food used by the amount of dog food eaten by each dog.
Hence, x =
x =
x =5
A negative exponent is the opposite of a regular exponent so for example, 5 to the power of -3 is 1/125
