Answer:
36x
Step-by-step explanation:
You do 12 x 3 which equals 36. Then you add the x at the end.
Answer:
Explanation:
x - 7y = 7
-7y = -x + 7
y = (-1/-7)x + 7/-7
y = (1/7)x - 1
6x - 7y = -28
-7y = -6x - 28
y = (-6/-7)x - 28/-7
y = (6/7)x + 4
The answer to 89+27+11 is 127
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 
.
In such type of questions, all that you are supposed to do is, use basic mathematics to eliminate any one of the given two variables.
Check out the equations if in case you can multiply any of the given ones with a -1 and add the two equations,eliminating one of the variables.
