1. The problem statement, all variables and given/known data The question states: "find all scalars c, if any exist such that given statement is true." It also suggests trying to do without pencil and paper. a) vector [c2, c3, c4] is parallel to [1,-2,4] with same direction. b) vector [13, -15] is a linear combination of vectors [1,5] and [3,c] c) vector [-1,c] is a linear combination of vectors [-3,5] and [6,-11] 3. The attempt at a solution a) for it to be parallel, it has to be a scalar multiple of [1,-2,4] = x. and [c2, c3, c4] = y. then you can say ax = y. but wouldn't that give different values for all 3 c's? Lets say for example a=2. then 2x = y. then it would be: i) c2 = 2*1 ii) c3 = 2*-2 iii) c4 = 2*4 which results in a different value of c in each. can i conclude that there DNE a such c? b) the scalar multiple could be any real number for both vectors so c could be any real number? c) 1[-3,5] + 1/3[6,-11] = [-1,4/3] so c = 4/3. this was achieved by trial and error. firstly is this even right? second, if its right, is there a algebraic way of doing it. it would have 3 unknowns and 2 equations. at a glance seems pretty simple, or i just forgot some of the things i learned last year. any guidance would be appreciated.