(Solved): with explanation please True of false: 1. Let L:R6R4 be a linear transformation. Then the kern ...

with explanation please

True of false: 1. Let $$L:{\mathbb{R}}^6?{\mathbb{R}}^4$$ be a linear transformation. Then the kernel of $$L$$ has dimension more than 1. 2. A set of 5 polynomials in $$P_3$$ are always linearly dependent. 3. $$P_5$$ and $$M_{23}$$ are isomorphic vector spaces. 4. Let $$T$$ and $$S$$ be two nonempty subsets of a vector space $$V$$ such that $$S$$ is contained in $$T$$. If $$S$$ is linearly dependent, so is $$T$$. 5. Let $$T$$ and $$S$$ be two nonempty subsets of a vector space $$V$$ such that $$S$$ is contained in $$T$$. If $$T$$ is linearly dependent, so is $$S$$. 6. Let $$L:P_2?{\mathbb{R}}^3$$ be the map defined by $$L(\overrightarrow{0}+?)+U$$