Answer:
Step-by-step explanation:
The question to be solved is the following :
Suppose that a and b are any n-vectors. Show that we can always find a scalar γ so that (a − γb) ⊥ b, and that γ is unique if 
. Recall that given two vectors a,b a⊥ b if and only if 
where 
is the dot product defined in 
. Suposse that 
. We want to find γ such that 
. Given that the dot product can be distributed and that it is linear, the following equation is obtained
Recall that 
are both real numbers, so by solving the value of γ, we get that
By construction, this γ is unique if 
, since if there was a 
such that 
, then
Question Two is D. $14.80
Given:
Total students = 60
Student passed = 85%
To find:
The number of students who failed and then convert it in %.
Solution:
We have,
Number of passed student = 85% of Total students
= 
= 
So, number of passes students is 51.
Number of students who failed = Total students - Passes students
= 
= 
So, number of students who failed is 9.
Therefore, 15% students fail in the test.
Net Income: I=$1,240.00
Food: F=$150.00
Car payment: C=$244.00
Rent: R=$300.00
Saving: S=$50.00
Other things: O=?
F+C+R+S+O=I
$150.00+$244.00+$300.00+$50.00+O=$1240.00
Solving for O:
$744.00+O=$1240.00
$744.00+O-$744.00=$1240.00-$744.00
O=$496.00
Percent of his net income Victor can spend on other things: P=?
P=(O/I)*100%
P=($496.00/$1240.00)*100%
P=(0.40)*100%
P=40%
Answer: 40% of his net income Victor can spend on other things.
