Question: Exercise I (3 x 5 = 15 points) The following statements are false. Clearly explain why. 1. Let V = {(a1, a2) : a1, a2

Exercise I (3 x 5 = 15 points) The following statements are false. Clearly explain why. 1. Let V = {(a1, a2) : a1, a2 ( R}. Vector addition is the same, but scalar multiplication is different: for ce R and (a1, a2) E R, let c(a1, a2) = (0, a2). V is a vector space over R with these operations. 2. The system below is solvable as long as b2 = 2b1 only, and the column space is a plane in RK. 61 00 IF NAN b2 C3 b3 2 0 3. Let A = 0 1 0 Then the variables x2 and x4 in a vector a = (21, 22, 23, 24) E NulA are free. O

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