Linda Seales

Answered

2022-01-05

Show that the xy plane $W=(x,y,0)$ in $\mathbb{R}}^{3$ is generated by

(i)$u=\left[\begin{array}{c}1\\ 2\\ 0\end{array}\right]$ and $v=\left[\begin{array}{c}0\\ 1\\ 0\end{array}\right]$ (ii) $u=\left[\begin{array}{c}2\\ -1\\ 0\end{array}\right]$ and $v=\left[\begin{array}{c}1\\ 3\\ 0\end{array}\right]$

(i)

Answer & Explanation

Louis Page

Expert

2022-01-06Added 34 answers

Let

Comparing both side we get

Now from

Therfore, for any

Therefore, W is generated by u and v.

Let

Comparing both side we get

and

Now we solve equationn (1) and (2) to find the value of a and b. From (1) and (2), we get

Now from (2)

Therfore, for any

Therefore, W is generated by u and v.

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