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(A) For any vector $w$ in a plane to be represented as a linear combination $w = au + bv$ of two vectors $u$ and $v$ in that same plane,the vectors $u

Vedclass · Accepted Answer

None of $u$ and $v$ is a scalar multiple of the other

Vedclass · Answer

(A) For any vector $w$ in a plane to be represented as a linear combination $w = au + bv$ of two vectors $u$ and $v$ in that same plane,the vectors $u$ and $v$ must be linearly independent. Two vectors are linearly independent if and only if they are not parallel to each other. This means that neither $u$ can be written as $k \cdot v$ nor $v$ can be written as $k \cdot u$ for any scalar $k$. Therefore,the condition is that none of $u$ and $v$ is a scalar multiple of the other. Thus,option $A$ is the correct answer.

Let $u$ and $v$ be two vectors in a plane. Then any vector $w$ in the plane can be written as $w = au + bv$ for some scalars $a$ and $b$ if and only if

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