Express the vector $v = \begin{bmatrix}49\\0\end{bmatrix}$ as a linear combination of $x = \begin{bmatrix}6\\5\end{bmatrix}$ and $y = \begin{bmatrix}-5\\4\end{bmatrix}$
$v = $ ____ $x + $ ______$y$
How exactly can I express this vector as a linear combination of these other two vectors? I've never seen a problem like this before. Nor do I know exactly what a Linear Combination is in "laymans terms"
Best Answer
Just put: $$v = ax+by $$ then solve for $a$ and $b$ \begin{cases} 6a-5b = 49\\ 5a+4b = 0 \end{cases} You will get: $$v = 4x-5y$$