Question: 2. Let A be an m x 13 matrix. Denote by (33- the vector in R with all components zero except for a 1 in

2. Let A be an m x 13 matrix. Denote by (33- the vector in R\" with all components zero except for a 1 in the jth position. Suppose that the system of equations AX = 83' has a solution for each j = 1, 2, . . . , m. (a) Show that A has rank m if and only if the system of equations AX = 133- has a solution for each 3' =1, 2, . . . ,m. (b) Suppose that n

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