In the following problems, make sure to write your arguments coherently in full sentences. If pos-…

In the following problems, make sure to write your arguments coherently in full sentences. If pos- sible, start a sentence with words rather than a formula. Avoid using ambiguous symbols such as +, ?, …,.Instead, use words to transition your ideas, for example “This leads to”, “Therefore”, “We want to show”, etc. Consider the following subspaces of R3: U V W = = = {(x21, 12, 13): 21 = 22 +23}, {(21, 22, 23) : *1 = 22}, {({1, 12, 13): 21 = 12 = 13}. 1. Find a basis of the intersection U V. What is the dimension? Convention: the basis of the {0} vector space is (the empty set) and its dimension is 0.