Find the Specified Change-Of-Coordinates Matrix $B = \left\{ \mathbf { b } _ { 1 } , \mathbf { b } _ { 2 } \right\}$

question 34

Multiple Choice

Find the specified change-of-coordinates matrix.
-Consider two bases $B = \left\{ \mathbf { b } _ { 1 } , \mathbf { b } _ { 2 } \right\}$ and $C = \left\{ \mathbf { c } _ { 1 } , \mathbf { c } _ { 2 } \right\}$ for a vector space $V$ such that $\mathbf { b } _ { 1 } = \mathbf { c } _ { 1 } - 5 \mathbf { c } _ { 2 }$ and $\mathbf { b } _ { 2 } = 2 \mathbf { c } _ { 1 } - 4 c _ { 2 }$ . Find the change-of-coordinates matrix from $B$ to $C$ .

• A)
• \(\left[ \begin{array} { r r } 1 & 2 \\ - 5 & - 4 \end{array} \right]\)
• B)
• \(\left[ \begin{array} { l l } 1 & - 5 \\ 2 & - 4 \end{array} \right]\)
• C)
• \(\left[ \begin{array} { l l } 1 & 2 \\ 5 & 4 \end{array} \right]\)
• D)
• \(\left[ \begin{array} { r r } 0 & 2 \\ - 5 & - 4 \end{array} \right]\)

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