4. Let \(\vec{v}^1 = (1, 3, 5)\), \(\vec{v}^2 = (-2, 1, 7)\) and let P be the plane spanned by \(\vec{v}^1\) and \(\vec{v}^2\). (That is, P = \(\langle \vec{v}^1, \vec{v}^2 \rangle\)). Let \(\vec{v}^3 = (7, 7, 1)\). Show that \(\langle \vec{v}^1, \vec{v}^2, \vec{v}^3 \rangle\) as follows:
• First show that \(\vec{v}^3\) is in P.
• Next explain why \(\langle \vec{v}^1, \vec{v}^2, \vec{v}^3 \rangle\) is a subspace of P.
• Next explain why P = \(\langle \vec{v}^1, \vec{v}^2 \rangle\) is a subspace of \(\langle \vec{v}^1, \vec{v}^2, \vec{v}^3 \rangle\).
• Conclude that \(\langle \vec{v}^1, \vec{v}^2, \vec{v}^3 \rangle\) is the exact same set as P
