Hey navathi.

If a vector is spanned by something, it means it can be written as a linear combination of those vectors and if this is the case, it means that these vectors become the columns in a matrix A where Ax = b where you have A and b and you want to find x.

However, in this case the vectors you have provided are not linearly independent but only two are linearly independent (I used Octave to show this, but you can do this by converting these vectors to reduced row echelon form).

So now you augment this system with your vector, but in order for the solution to be not inconsistent you need the last row to make sense which means that lambda will have to take a particular value to not make this in-consistent.