2.4 Homework problems Q1 Let B = (b , b2,..., b-1, br, br+1..., bn be a non-singular matrix. If col- umn bis replace by a and that the resulting matrix is called B, along with a = S y b, then state...

2.4 Homework problems Q1 Let B = (b , b2,..., b-1, br, br+1..., bn be a non-singular matrix. If col- umn bis replace by a and that the resulting matrix is called B, along with a = S y b, then state the necessary and sufficient condition for B, to be non-singular. Q2 Let V be a finite dimensional vector space over R. If S is a set of elements in V such that Span(S) = V, what is the relationship between S and the basis of V? Q3 Let T:R ? R$ be defined by T:21, 12, 13) = (-01-12 +2.13, 2.11 +22, -21 - 2202 + 2.) then, 1. show that T is a linear transformation 2. what are the conditions on a, b, c such that (a, b,c) is in the null space of T. Specifically, find the nullity of T. Q4 Construct a linear transformation T: V W , where V and W are vector spaces over F such that the dimension of the kernel space of T is 666. Is such a transformation unique? Give reasons for your answer.

Jan 05, 2022
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