Which of the following are actually vector spaces over the real numbe.pdf
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The document discusses which sets are vector spaces over the real numbers, identifying correct choices regarding the complex numbers and polynomials of even degree, as well as continuous functions. It highlights the usefulness of the Mathematica command 'rowreduce[]' for solving linear equations and finding matrix inverses. The conclusion affirms that options reflecting the correct vector spaces include both complex numbers and continuous functions.
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![Which of the following are actually vector spaces over the real numbers? The complex numbers
The set of all polynomials of even degree. All continuous functions for which integral^1_0 f(x)
dx =0. All vectors of the form (a, b, l) where a and b are any real numbers. I & II I&III; I & IV
II & III II & IV The mathematica command "RowReduce[] is a very useful tool in solving a
system of linear equations. finding the inverse of a matrix. finding the dimension of the range of
a transformation. computing the determinant of a matrix. determining if a set of vectors is
linearly independent. I only I & II only I, II & III only All but IV All but V
Solution
3. The statements I and III are correct because complex numbers form a vector space as well as
all coontinuous functions form a vector space
4. Row reduce is very usful tool in solving system of liner equations and finding the inverse of a
matrix. So statement I and II are correct.](https://image.slidesharecdn.com/whichofthefollowingareactuallyvectorspacesovertherealnumbe-230706185022-4256a1d3/85/Which-of-the-following-are-actually-vector-spaces-over-the-real-numbe-pdf-1-320.jpg)
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Which of the following are actually vector spaces over the real numbe.pdf
- 1. Which of the following are actually vector spaces over the real numbers? The complex numbers The set of all polynomials of even degree. All continuous functions for which integral^1_0 f(x) dx =0. All vectors of the form (a, b, l) where a and b are any real numbers. I & II I&III; I & IV II & III II & IV The mathematica command "RowReduce[] is a very useful tool in solving a system of linear equations. finding the inverse of a matrix. finding the dimension of the range of a transformation. computing the determinant of a matrix. determining if a set of vectors is linearly independent. I only I & II only I, II & III only All but IV All but V Solution 3. The statements I and III are correct because complex numbers form a vector space as well as all coontinuous functions form a vector space 4. Row reduce is very usful tool in solving system of liner equations and finding the inverse of a matrix. So statement I and II are correct.