Find all values of such that and

MATHEMATICS · Subjective · IB Diploma Programme · Mathematics: Applications and Interpretation · Number and Algebra · Number and Algebra

Problem

Find all values of

\lambda

such that

x, y, z \neq (0, 0, 0)

and

(\hat{i} + \hat{j} + 3\hat{k})x + (3\hat{i} - 3\hat{j} + \hat{k})y + (-4\hat{i} + 5\hat{j})z = \lambda(x\hat{i} + y\hat{j} + z\hat{k})

, where

\hat{i}, \hat{j}

and

\hat{k}

are unit vectors along the coordinate axes.