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 
.
I think the correct answer from the choices listed above is option D. A polynomial function has a zero value at x=3 for the <span>expression where one factor is x-3. This factor when x=3 will always result to a zero value no matter what you multiply to it. Hope this answers the question.</span>
Answer: y > x, y > 2
The horizontal line goes through 2 on the y axis. This boundary line is represented by the equation y = 2, since every point on this line has a y coord of 2. The shading above it means that the inequality is y > 2. Every point in the shaded region of y > 2 has a y coord that is larger than 2.
The other inequality is y > x because we shade above the dashed boundary line y = x, which is that slanted dashed line.
Combining the two regions of y > 2 and y > x leads to what is shown.
Hello there.
Answer: Work out the volume of both:
20 x 15 x 10 = 3000
3 x 3 x 3 = 27.
Subtract the inside part:
3000 - 27 = 2973.
Hope This Helps You!
Good Luck Studying ^-^
