What is the dimension of \(\mathbb R^4\)?

What is the dimension of the line span(\((2, 4, 6)\)) in \(\mathbb R^3\)?

What is the dimension of the xy-plane in \(\mathbb R^3\)?

Find the dimension of the subspace S = {\((x, y, z)\) in \(\mathbb R^3\) : x + y + \(z=0\)}.

Find the dimension of span(\((1, 0, 0)\), \((0, 1, 0)\), \((1, 1, 0)\)).

Find the dimension of span(\((1, 2)\), \((2, 4)\), \((3, 6)\)) in \(\mathbb R^2\).

A subspace of \(\mathbb R^5\) has a basis with three vectors. What is its dimension?

Can a subspace of \(\mathbb R^3\) have dimension 4? Explain.

Find the dimension of the zero subspace {0} in \(\mathbb R^n\).

A learner says the dimension of a subspace is the number of vectors used to describe it. Diagnose the error using span(\((1,0)\), \((0,1)\), \((1,1)\)).