Answer:
Additive Inverse Property.
Step-by-step explanation:
the value that brings you back to the identity element under addition
So a+-a=0
Hope this helps!!!
~BBGLUVER
It’s -3,-2 hope thiisssss helpsssss
Answer:
(- 4, 1 )
Step-by-step explanation:
A translation (x + 1), y - 3 ) means add 1 to the original x- coordinate and subtract 3 from the original y- coordinate.
B = (- 5, 4 ), thus
B' = (- 5 + 1, 4 - 3 ) = (- 4, 1 )
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:
1.25 liters of oil
Step-by-step explanation:
Volume in Beaker A = 1 L
Volume of Oil in Beaker A = 1*0.3 = 0.3 L
Volume of Vinegar in Beaker A = 1*0.7 = 0.7 L
Volume in Beaker B = 2 L
Volume of Oil in Beaker B = 2*0.4 = 0.8 L
Volume of Vinegar in Beaker B = 1*0.6 = 1.2 L
If half of the contents of B are poured into A and assuming a homogeneous mixture, the new volumes of oil (Voa) and vinegar (Vva) in beaker A are:

The amount of oil needed to be added to beaker A in order to produce a mixture which is 60 percent oil (Vomix) is given by:

1.25 liters of oil are needed.