# When two column vector in R2 are equal? Give an example. Computer u + 3v, u – 2v, whereu = $$\begin{bmatrix}1\\ -3\\ 2\end{bmatrix}$$, v = $$\begin{bmatrix}1\\ -1\\ 3\end{bmatrix}$$

Solution:

Given,

u = $$\begin{bmatrix}1\\ -3\\ 2\end{bmatrix}$$

v = $$\begin{bmatrix}1\\ -1\\ 3\end{bmatrix}$$

Now,

u + 3v = $$\begin{bmatrix}1\\ -3\\ 2\end{bmatrix}$$ + 3 $$\begin{bmatrix}1\\ -1\\ 3\end{bmatrix}$$

= $$\begin{bmatrix}1\\ -1\\ 3\end{bmatrix}$$ + $$\begin{bmatrix}3\\ -3\\ 9\end{bmatrix}$$

= $$\begin{bmatrix}1+3\\ -1-3\\ 3+9\end{bmatrix}$$

= $$\begin{bmatrix}4\\ -4\\ 12\end{bmatrix}$$

Again,

u – 2v = $$\begin{bmatrix}1\\ -3\\ 2\end{bmatrix}$$ – 2 $$\begin{bmatrix}1\\ -1\\ 3\end{bmatrix}$$

= $$\begin{bmatrix}1\\ -3\\ 2\end{bmatrix}$$ – $$\begin{bmatrix}2\\ -2\\ 6\end{bmatrix}$$

= $$\begin{bmatrix}1-2\\ -3-2\\ 2-6\end{bmatrix}$$

= $$\begin{bmatrix}-1\\ -5\\ -4\end{bmatrix}$$