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Mathematics, 28.11.2019 23:31 chrisraptorofficial

Are the following sets vector spaces with the indicated operations? if not ,why not?

1) the set v of non negative real numbers, ordinary addition and scalar multiplication.
2) the set of all polynomials of degree < =3; operations of p.
3) the set v of all 2x2 matrices of the form [ab][0c]; operations of m22
4) the set v of 2x2 matrices with zero determinant; usual matrix operations

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Are the following sets vector spaces with the indicated operations? if not ,why not?

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