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Linear Algebra

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Find Coordinate Vector

LINALG-GER1UG

$$ {\cal B}=\left \{\left [ \matrix { 1\cr 4}\right ], \left [\matrix { 4 \cr 1}\right ] \right \}$$

...is a basis for $R^2$.

$$\vec v=\left [\matrix {4 \cr 4}\right ]$$

...is an element of $R^2$.

Suppose that:

$$\vec x=\left [\matrix { a \cr b}\right ]$$

...is the coordinate vector for $\vec v$ relative to ${\cal B}$.

Find the components of $\vec x$.