Let v1,...,vk,u,w be vectors in linear space V.
Given that the equation: x1v1+....+xkvk=u has a single solution, and the equation: x1v1+....+xkvk=w has no solution.
Find the dimension of: Sp{v1,....,vk,w}
So what I don't understand here is if we look at the narrow coefficient matrix, from the first given equation we can conclude that non of the rows reset and v1,....,vk are linear independent, but from the second given equation we can conclude that one or more rows resent and that v1,....,vk are linear dependent. Isn't it a contradiction?
Given that the equation: x1v1+....+xkvk=u has a single solution, and the equation: x1v1+....+xkvk=w has no solution.
Find the dimension of: Sp{v1,....,vk,w}
So what I don't understand here is if we look at the narrow coefficient matrix, from the first given equation we can conclude that non of the rows reset and v1,....,vk are linear independent, but from the second given equation we can conclude that one or more rows resent and that v1,....,vk are linear dependent. Isn't it a contradiction?