Linear Algebra Examples

Find the Norm [[0+1i],[1+1i],[4-2i]]
Step 1
The norm is the square root of the sum of squares of each element in the vector.
Step 2
Simplify.
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Step 2.1
Multiply by .
Step 2.2
Add and .
Step 2.3
Use the formula to find the magnitude.
Step 2.4
Raising to any positive power yields .
Step 2.5
One to any power is one.
Step 2.6
Add and .
Step 2.7
Any root of is .
Step 2.8
One to any power is one.
Step 2.9
Multiply by .
Step 2.10
Use the formula to find the magnitude.
Step 2.11
One to any power is one.
Step 2.12
One to any power is one.
Step 2.13
Add and .
Step 2.14
Rewrite as .
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Step 2.14.1
Use to rewrite as .
Step 2.14.2
Apply the power rule and multiply exponents, .
Step 2.14.3
Combine and .
Step 2.14.4
Cancel the common factor of .
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Step 2.14.4.1
Cancel the common factor.
Step 2.14.4.2
Rewrite the expression.
Step 2.14.5
Evaluate the exponent.
Step 2.15
Use the formula to find the magnitude.
Step 2.16
Raise to the power of .
Step 2.17
Raise to the power of .
Step 2.18
Add and .
Step 2.19
Rewrite as .
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Step 2.19.1
Factor out of .
Step 2.19.2
Rewrite as .
Step 2.20
Pull terms out from under the radical.
Step 2.21
Apply the product rule to .
Step 2.22
Raise to the power of .
Step 2.23
Rewrite as .
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Step 2.23.1
Use to rewrite as .
Step 2.23.2
Apply the power rule and multiply exponents, .
Step 2.23.3
Combine and .
Step 2.23.4
Cancel the common factor of .
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Step 2.23.4.1
Cancel the common factor.
Step 2.23.4.2
Rewrite the expression.
Step 2.23.5
Evaluate the exponent.
Step 2.24
Multiply by .
Step 2.25
Add and .
Step 2.26
Add and .
Step 3
The result can be shown in multiple forms.
Exact Form:
Decimal Form: