calculus

Define vector space

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In a finite dimensional vector space V of dimension n, subset A of V has n number of linearly independent elements. Then

• A is generating set of V

• A is not a generating set of V

• Removing some elements from A can give generating set.

• Adding some elements to A can give basis

How many special solutions are there in a matrix operation:

• They are equal to the number of pivot columns

• They are equal to the number of free columns

• 3x

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• (-1/5,1)

• (1/5,0)

• (1/5,-1)

• (-1/5,-1)