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eclass.srv.ualberta.ca 2 of 2 1. Consider the matrix 3-2 1 4-1 2 3 5 7 8...


eclass.srv.ualberta.ca 2 of 2 1. Consider the matrix 3-2 1 4-1 2 3 5 7 8 (a) Find a basis B for the null space of A. Hint: you need to verify that the vectors you propose 20 actually form a basis for the null space. (Recall: (1) the null space of A consists of all x e R with Ax = 0, and (2) the matrix equation Ax = 0 is equivalent to a certain system of linear equations.) 151 (b) Does a linear combination of the vectors in B belong to the null space of A?-Explain! (c) From among the standard basis vectors e,..., e, for R select suitable vectors to supplement 10 B from part (a) to a basis of RD.
eclass.srv.ualberta.ca 2 of 2 1. Consider the matrix 3-2 1 4-1 2 3 5 7 8 (a) Find a basis B for the null space of A. Hint: you need to verify that the vectors you propose 20 actually form a basis for the null space. (Recall: (1) the null space of A consists of all x e R with Ax = 0, and (2) the matrix equation Ax = 0 is equivalent to a certain system of linear equations.) 151 (b) Does a linear combination of the vectors in B belong to the null space of A?-Explain! (c) From among the standard basis vectors e,..., e, for R select suitable vectors to supplement 10 B from part (a) to a basis of RD.
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