1. (12 points) Answer True or False for each of the following questions. There i

Question

1. (12 points) Answer True or False for each of the following questions. There is no need to justify your answer. (a) If A is an n × m, matrix and B is m × r matrix then the domain of AB (viewed as a transformation) is Rn and the codomain is R" (b) If the product AB of two matrices is defined, then each column of AB is a linear combination of the columns of A using weights from the corresponding column of (c) If A is an n × n matrix such that the columns of A span R", then the row reduced echelon form of A is In (d) Given a linear transformation T:V ? W, where V and W are vector spaces, then the zero vector is always in Nul T. (e) The set (1,t-2,t 2,3t2 +7) is a basis for P2 (the vector space of polynomials of degree 2 or less.) (f) Suppose the set fbi, b2, ba) is a basis for a vector space V. It is possible to find a set with less than 3 vectors in V that spans V

Explanation / Answer

Solutiob - Part (a):

If a matrix A is n x m and B is m x r. the AB is n x r. So AB take a vector of dimension r and produces a vector of dimension n. So the given statement is wrong.

Answer: False.

I suppose option (a) marked to answer only.  

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