Linear Algebra Examples

Find the Distance Between the Vectors
Step 1
The distance between two vectors and in is defined to be which is the Euclidean norm of the difference .
Step 2
Find the norm of the difference where and .
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Step 2.1
Create a vector of the difference.
Step 2.2
The norm is the square root of the sum of squares of each element in the vector.
Step 2.3
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Step 2.3.1
Subtract from .
Step 2.3.2
Raising to any positive power yields .
Step 2.3.3
Subtract from .
Step 2.3.4
Raise to the power of .
Step 2.3.5
Add and .
Step 2.3.6
Raise to the power of .
Step 2.3.7
Add and .
Step 2.3.8
Add and .
Step 3
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
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