The linear rank theorem an example Consider the linear trans

The linear rank theorem: an example. Consider the linear transformation F : R^4 rightarrow R^3 defined by Find a basis {v_1, v_2, v_3, v_4} of R^4 and a basis {w_1, w_2, w_3} of R^3 such that F(V_j) = where r is the rank of F. Do this as follows: First find a basis {v_3, v_4} of S = ker (F). (We have done this in class and on HW 11.). This shows that the nullity of F is two, and the rank r of F is also two (why?). Then find a basis {v_1, v_2} of T = S^. (Compare the previous problem, and the problem below.) Then {v_1, v_2, v_3, v_4} is a basis of R^4 (why?). Then put w_1 = F (v_1) and w_2 = F (v_2) and find vector w_3 which is not in span {w_1, w_2}.

Solution

Please ask this question in precalculas or Statistics to get a better answer.

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