Mathematics II207510 marksNumerical: linear independence and basisLinearly independent sets
Define linearly independent set of vectors with an example. Show that the vectors (1,4,3), (0,3,1) and (3,-5,4) are linearly independent. Do they form a basis? Justify.
Define linearly independent set of vectors with an example. Show that the vectors (1,4,3), (0,3,1) and (3,-5,4) are linearly independent. Do they form a basis? Justify.[10]
A set of vectors ${\mathbf{v1}, \mathbf{v2}, \ldots, \mathbf{vn}}$ in a vector space $V$ is linearly independent if the only solution to $$x1\mathbf{v1} + x2\mathbf{v2} + \cdots + xn\mathbf{vn} = \mathbf{0}$$ is the trivial solution $x1 = x2 = \cdots = xn = 0$. If some nontrivial solution exist...