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Fed [463]
3 years ago
7

Consider the following. {(1, −6, 3, 2), (1, 2, 0, 6)}

Mathematics
1 answer:
andre [41]3 years ago
8 0

Answer:  The required answers are

(a) NOT orthogonal.

(b) NOT orthonormal.

(c) Not a basis,

Step-by-step explanation:  We are given to consider the vectors {(1, −6, 3, 2), (1, 2, 0, 6)}.

(a) We are to determine whether the set of vectors in \mathbb{R}^n is orthogonal.

(b) If the set is orthogonal, then to determine whether it is also orthonormal.

(c) To determine whether the set is a basis for \mathbb{R}^n.

We know that

any two vectors u and v are orthogonal, if their dot product u.v is zero.

The dot product of (1, −6, 3, 2) and (1, 2, 0, 6) is given by

(1,-6,3,2).(1,2,0,6)=1\times1+(-6)\times2+3\times 0+2\times6=1-12+0+12==1\neq 0.

So, the given set is not orthogonal.

Since the vectors are not orthogonal, they cannot be orthonormal.

To be a basis of \mathbb{R}^n, the set must contain n vectors.

Here, we are dealing with \mathbb{R}^4, and the set contains only 2 vectors.

So, the given set cannot be a basis.

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Answer:

B.

Step-by-step explanation:

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So first we must find 3.5% of 16. 3.5% in decimal form is 0.035, since you divide 3.5 by 100. Then, when you multiply 0.035 by 16, you get 0.56. Since the solution decreased by that percentage, you must subtract 0.56 from 16, which is 15.44.

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Step-by-step explanation:

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Answer:

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