MTH1004 Linear Algebra Tutorial Class 2

Question 1

Question

Using Gauss-Jordan elimination: (i) Determine whether the vector $u=\left[\begin{array}{c}9\\ 0\\ 4\end{array}\right]$ belongs to the span of the following vectors: $v=\left[\begin{array}{c}1\\ 2\\ 4\end{array}\right]$, $w=\left[\begin{array}{c}2\\ -1\\ -1\end{array}\right]$, $z=\left[\begin{array}{c}-3\\ 1\\ 1\end{array}\right]$. (ii) Show that the vectors $u=\left[\begin{array}{c}1\\ -1\\ 2\end{array}\right]$, $v=\left[\begin{array}{c}-3\\ 2\\ 4\end{array}\right]$, $w=\left[\begin{array}{c}-2\\ 1\\ 6\end{array}\right]$ are linearly dependent and simplify span(u, v, w) in terms of u, v, w.

Solution

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Question 2

Question

For what $k$ values will the systems: (a) $nkx+2y=3$, $2x-4y=-6$, (b) $nx+ky=1$, $kx+y=1$ have: (i) infinitely many solutions, (ii) no solutions, and (iii) a unique solution? For (i) write the set of solutions.

Solution

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