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3. Let $v_1$ and $v_2$ be vectors in $V$. (a) Prove that {$v_1$} is linearly independent if and only if $v_1 eq 0$. (b) Prove that {$v_1, v_2$} is linearly dependent if and only if $v_1$ is a scalar multiple of $v_2$ or $v_2$ is a scalar multiple of $v_1$.

          3. Let $v_1$ and $v_2$ be vectors in $V$.
(a) Prove that {$v_1$} is linearly independent if and only if $v_1 
eq 0$.
(b) Prove that {$v_1, v_2$} is linearly dependent if and only if $v_1$ is a scalar multiple of $v_2$ or $v_2$ is
a scalar multiple of $v_1$.

3. Let v1 and v2 be vectors in V.
(a) Prove that v1 is linearly independent if and only if v1
eq 0.
(b) Prove that v1, v2 is linearly dependent if and only if v1 is a scalar multiple of v2 or v2 is
a scalar multiple of v1.

Added by Lisa S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/03/2023

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3. Let v1 and v2 be vectors in V. (a) Prove that {v1} is linearly independent if and only if v1 ≠ 0. (b) Prove that {v1, v2} is linearly dependent if and only if v1 is a scalar multiple of v2 or v2 is a scalar multiple of v1.