Mumbai University > Electronics and Telecommunication > Sem 4 > Applied Maths 4

Marks: 4M

Year: Dec 2014

Here the element W $\neq$ {[a, i, 1] | a $\in$ R}, as i is an imaginary term

Hence we consider W = {[a, 1, 1] | a $\in$ R}

Let $v_{1} = (a_{1}, 1, 0)$ and $v_{2} = (a_{2}, 1, 1)$ be the two vectors in $R^3$

Now $v_{1} + v_{2} = (a_{1}, 1, 1) + (a_{2}, 1, 1) = (a_{1} + a_{2}, 1, 1)$

Since $a_{1} + a_{2} \in R, v_{1} + v_{2}$ is in $R^3$

If k is any scalar then $kv_{1} = k(a_{1}, 1, 1) = (ka_{1}, 1, 1)$

Hence, $kv_{1}$ is also in $R^3$

Hence, W = {[a, 1, 1] | a $\in$ R} is a subspace of $R^3$