If a and b are two non-zero and non-collinear | vedclass

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(B) Let $x(a + b) + y(a - b) = 0$ for some scalars $x$ and $y$.This can be rewritten as $(x + y)a + (x - y)b = 0$.Since $a$ and $b$ are non-collinear,

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Linearly independent vectors

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(B) Let $x(a + b) + y(a - b) = 0$ for some scalars $x$ and $y$.This can be rewritten as $(x + y)a + (x - y)b = 0$.Since $a$ and $b$ are non-collinear,they are linearly independent.Therefore,the coefficients must be zero:$x + y = 0$ and $x - y = 0$.Adding these equations gives $2x = 0$,so $x = 0$.Substituting $x = 0$ into $x + y = 0$ gives $y = 0$.Since the only solution is $x = 0$ and $y = 0$,the vectors $a + b$ and $a - b$ are linearly independent.

If $a$ and $b$ are two non-zero and non-collinear vectors,then $a + b$ and $a - b$ are:

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