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104 Quiz LA-01 Name: SID# 1. True and False (Justify your answer by given a logical argument or a counterexample). (a) x y 1 c an be represented geometrically as a plane through the origin in 2-dimention space. 1 0 (b) All linear combination of the vector A 0 and B 2 can fill a plane of a 0 0 3-dimention space. (c) Multiplication of matrices, whenever defined, is commutative. (d) The multiplication of an n n and an m m matrices is an n m matrix. (e) If rows 1 and 3 of A are the same, so are rows 1 and 3 of AB. (f) The equations 2x 3 y 0 can’t be solved in the point of view of column picture. 3x 5 y 0 (g) Suppose that w is a solution to Ax = b, where b k(u + w) is a solution to Ax =b. 0, and u is a solution to Ax = 0. Then 2. Consider the following linear equations Ax=b, (a) Find the elimination matrices E21 , E31 , E41 E32 , E42 and E43 that produce the following matrix A to an upper triangular matrix U. (20%) (b) Find the solution, if the unique solution exists. (10%) 2 1 1 2 Ax 2 0 3 6 0 2 0 0 1 2 x 0 1 0 0 3 1 計算題點名 2-(a) TA: U0321104 2-(b) TA: U0321142