Question

If a and b are non-collinear vectors and A = (x+y)a + (2x + y+1)b. Find x and y

Answer 1

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Answer on Question #74191 – Math – Linear Algebra

Question

If $a$ and $b$ are non-collinear vectors and $A = (x + y)a + (2x + y + 1)b$. Find $x$ and $y$.

Solution

$$(x + y) \bar{a} + (2x + y + 1) \bar{b} = 0;$$

Because vectors $\bar{a}$ and $\bar{b}$ are non-collinear,

$$\left\{ \begin{array}{c} x + y = 0, \\ 2x + y + 1 = 0; \end{array} \right.$$ $$\left\{ \begin{array}{c} x = -y, \\ 2x + y + 1 = 0; \end{array} \right.$$ $$2(-y) + y + 1 = 0;$$ $$-2y + y + 1 = 0;$$ $$-y = -1;$$ $$y = 1;$$ $$x = (-y) = -1.$$

Answer: $x = -1; y = 1$.