For each of the following sets and operations on them, determine if it is a vector...
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For each of the following sets and operations on them, determine if it is a vector space. If it is not a vector space, give at least one reason why it is not. (a) Vi is the set of all vectors in R- in the first quadrant. Addition and scalar multiplication are defined normally. (b) V2 is the set of all polynomials p(t) such that p(0) = 0. Addition and scalar multiplication are defined normally. %3D (c) V3 is the set of all upper triangular 2 x 2 matrices. Addition is matrix addition, and scalar multiplication is normal matrix scalar multiplication. (d) V4 is the set of all 2 x 2 matrices. Addition is defined as matrix multiplication, and scalar multiplication is normal matrix scalar multiplication. For each of the following sets and operations on them, determine if it is a vector space. If it is not a vector space, give at least one reason why it is not. (a) Vi is the set of all vectors in R- in the first quadrant. Addition and scalar multiplication are defined normally. (b) V2 is the set of all polynomials p(t) such that p(0) = 0. Addition and scalar multiplication are defined normally. %3D (c) V3 is the set of all upper triangular 2 x 2 matrices. Addition is matrix addition, and scalar multiplication is normal matrix scalar multiplication. (d) V4 is the set of all 2 x 2 matrices. Addition is defined as matrix multiplication, and scalar multiplication is normal matrix scalar multiplication.
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