Let
be a set of orthogonal vectors. By definition of orthogonality, any pairwise dot product between distinct vectors must be zero, i.e.
Suppose there is some linear combination of the
such that it's equivalent to the zero vector. In other words, assume they are linearly dependent and that there exist
(not all zero) such that
(This is our hypothesis)
Take the dot product of both sides with any vector from the set:
By orthogonality of the vectors, this reduces to
Since none of the
are zero vectors (presumably), this means
. This is true for all
, which means only
will allow such a linear combination to be equivalent to the zero vector, which contradicts the hypothesis and hence the set of vectors must be linearly independent.
Answer:
Your answer is
<em>8</em><em>3</em><em>/</em><em>1</em><em>1</em><em> </em>
Hope this helped you
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Answer:
Step-by-step explanation:
and h(x)= 2x-8
g o h is a composition function
First we find g o h
g o h is g(h(x))
We plug in h(x) in g(x)
We replace x with 2x-8 in g(x)
To find domain we look at the domain of h(x) first
Domain of h(x) is set of all real numbers
now we look at the domain of g(h(x))
Negative number inside the square root is imaginary. so we ignore negative number inside the square root
So to find domain we set 2x - 12 >=0 and solve for x
2x - 12 >=0
add both sides by 12
2x >= 12
divide both sides by 2
x > = 6
Answer:
Length=18 Width=6
Step-by-step explanation:
Hello, You should first you algebra and and assign the dimensions with letters.
Length=x Width= 1/3x
as its the perimeter you add all the side together
x + x + 1/3x + 1/3x
which equals= 8/3x (this is an improper fraction at the moment)
then we know the total perimeter =48
so 48=8/3 x
so rearrange to get X by it's self
so 48 x 3/8
which x=18