Linear Algebra Quiz
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VECTOR SPACES & SUBSPACES
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Let B={b1⃗,b2⃗}B = \{\vec{b_1}, \vec{b_2}\} and C={c1⃗,c2⃗}C = \{\vec{c_1}, \vec{c_2}\} be bases for R2\mathbb{R}^2 where c1⃗=2b1⃗+b2⃗\vec{c_1} = 2\vec{b_1} + \vec{b_2} and c2⃗=b1⃗+3b2⃗\vec{c_2} = \vec{b_1} + 3\vec{b_2}. If [w⃗]C=(2−1)[\vec{w}]_C = \begin{pmatrix} 2 \\ -1 \end{pmatrix}, what is [w⃗]B[\vec{w}]_B?
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