MATH 310 Quiz: Math 310 Quiz 2
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For what value(s) of h is y a linear combination of v1 and v2? (in other words, for what values is it in the plane generated by v1 and v2?) To gure this out, we write down the augmented matrix corresponding to the vector equation and run row reduction. This matrix is already in echelon form, so we can tell whether there"s going to be a solution or not. The bottom row is a row of the form [ 0 0 | b ] with nonzero b (meaning there is no solution) unless. Thus if h = 1/2, there is a solution, and y is a linear combination of v1 and v2. For any other h, there are no solutions: describe all solutions of ax = 0 in parametric vector form, where. Lucky for us this matrix is already in reduced echelon form!
