Question

How to find the dimensions of vector space in mathematics?

Answer 1

hey.......
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The dimensions of a vector space is the cardinality of the minimal generating set which in linearly independent. Now for V.

we have a + c = 0 and b - c + 2d = 0 .

Now from first conditions we observe that c is dependent on a . And from the second conditions we see that b + 2d = c .Now if we assign any arbitrary value to a then the value for c is fixed and hence the value of b + 2d is fixed. Now you can assign any arbitrary value to b and then the value of d is fixed.

Hence { a , b } is a minimal generating set which is linearly independent.

Hence dim V = 2

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i hope this helps u.
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