Answer:
-5
Step-by-step explanation:
add them together (-4)+(-1) make a t chart it'll help you out
Q = 7m + 3n
R = 11 - 2m
S = n + 5
T = -m - 3n + 8
simplify Q + S - T
7m + 3n + n + 5 - (-m - 3n + 8) =
7m + 4n + 5 + m + 3n - 8
8m + 7n - 3 <====
Answer:
=3
Step-by-step explanation:
following the order of operations, whatever is in the parentheses gets done first. so you would add 13 + 2 and get 15. then you would subtract 9-4 and get 5. then you would divide the numbers that you got and get 3.
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:
4.8 Cups of salt and 14.4 cups of sugar
Step-by-step explanation: