Determine whether the ordered pair is a solution of the given inequality.
1 answer:
Answer:
No.
Step-by-step explanation:
Given:
The given inequality is:
Now, in order to check whether (1, 0) holds true for the inequality or not, we plug in 0 for 'y' and 1 for 'x' and check whether the inequality is logically correct or not. Thus,
So, the ordered pair (1, 0) is NOT a solution of the given inequality.
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Answer:
Take as the projection of u onto v and
as the vector such that b+w =u
Step-by-step explanation:
The formula of projection of a vector u onto a vector v is given by
, where
is the dot product between vectors.
First, let b ve the projection of u onto v. Then
We want a vector w, that is orthogonal to b and that b+w = u. From this equation we have that w = u-b = (-6,8)-\frac{-17}{25}(7,1)= \frac{1}{25}(-31,217)[/tex]
By construction, we have that w+b=u. We need to check that they are orthogonal. To do so, the dot product between w and b must be zero. Recall that if we have vectors a,b that are orthogonal then for every non-zero escalar r,k the vector ra and kb are also orthogonal. Then, we can check if w and b are orthogonal by checking if the vectors (7,1) and (-31, 217) are orthogonal.
We have that . Then this vectors are orthogonal, and thus, w and b are orthogonal.