Let vec{a} and vec{b} be two non-collinear ve | vedclass

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(B) Given the equation $2\vec{u} - \vec{v} = \vec{w}$.Substituting the expressions for $\vec{u}$,$\vec{v}$,and $\vec{w}$:$2(x\vec{a} + 2y\vec{b}) - (-

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$x = 10/7, y = 4/7$

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(B) Given the equation $2\vec{u} - \vec{v} = \vec{w}$.Substituting the expressions for $\vec{u}$,$\vec{v}$,and $\vec{w}$:$2(x\vec{a} + 2y\vec{b}) - (-2y\vec{a} + 3x\vec{b}) = 4\vec{a} - 2\vec{b}$$(2x\vec{a} + 4y\vec{b}) + (2y\vec{a} - 3x\vec{b}) = 4\vec{a} - 2\vec{b}$$(2x + 2y)\vec{a} + (4y - 3x)\vec{b} = 4\vec{a} - 2\vec{b}$Since $\vec{a}$ and $\vec{b}$ are non-collinear,we can equate the coefficients:$2x + 2y = 4 \Rightarrow x + y = 2$ (Equation $1$)$-3x + 4y = -2$ (Equation $2$)From Equation $1$,$x = 2 - y$. Substituting into Equation $2$:$-3(2 - y) + 4y = -2$$-6 + 3y + 4y = -2$$7y = 4 \Rightarrow y = 4/7$Substituting $y = 4/7$ into $x = 2 - y$:$x = 2 - 4/7 = 10/7$Thus,$x = 10/7$ and $y = 4/7$.

Let $\vec{a}$ and $\vec{b}$ be two non-collinear vectors. For what values of $x$ and $y$ is the equation $2\vec{u} - \vec{v} = \vec{w}$ true,where $\vec{u} = x\vec{a} + 2y\vec{b}$,$\vec{v} = -2y\vec{a} + 3x\vec{b}$,and $\vec{w} = 4\vec{a} - 2\vec{b}$?

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