Decide whether {\((1, 0)\), \((0, 1)\)} is linearly independent.

Decide whether {\((1, 2)\), \((2, 4)\)} is linearly independent.

Decide whether {\((1, 0, 0)\), \((0, 1, 0)\), \((0, 0, 1)\)} is linearly independent.

Decide whether {\((1, 1, 0)\), \((1, 0, 1)\), \((2, 1, 1)\)} is linearly independent.

Use a determinant to decide whether {\((1, 2)\), \((3, 4)\)} is linearly independent in \(\mathbb R^2\).

Explain why any set containing the zero vector is linearly dependent.

Can four vectors in \(\mathbb R^3\) be linearly independent? Explain.

Find a non-trivial linear relation among \((1, 2, 3)\), \((2, 4, 6)\), and \((0, 1, 0)\).

For which real t are \((1, t)\) and \((2, 4)\) linearly dependent?

A learner says a set is linearly independent if none of its vectors is zero. Diagnose the error.