Question

System of vectors $a_1,a_2,.......a_n$ is said to be linearly dependent if there exists a system of scalars $(c_1,c_2---c_{n}suchthat{c}_1\overline{a}+c_2\overline{a_2}+...c_n\overline{a_n}=\overline{0}$

• A. True
• B. False

Answer 1

The correct option is B False

Please read the given statement carefully. Are all the conditions required for linear dependence mentioned? No. Vectors $a_1,a_2.....a_n$ are linearly dependent if there exists a system of scalars $c_1,c_2....c_n$ such that $c_1\overline{a_1}+c_2\overline{a_2}+...c_n\overline{a_n}=\overline{0}$ But there is a condition on scalars that all of them can’t be zero simultaneously. At least one of them has to be non-zero. This is missing in the given statement. So it’s false.