MTH1004 Linear Algebra Tutorial Class 5

Question 1

Question

Prove that every line through the origin in ${\mathbb{R}}^3$ is a subspace of ${\mathbb{R}}^3$.

Solution

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Question 2

Question

Do the vectors $\left(\begin{array}{c}0\\ 1\\ 1\end{array}\right),\left(\begin{array}{c}1\\ 0\\ 1\end{array}\right),\left(\begin{array}{c}1\\ 1\\ 0\end{array}\right)$ form a basis for ${\mathbb{R}}^3$? And $\left(\begin{array}{c}0\\ 1\\ 1\end{array}\right),\left(\begin{array}{c}1\\ 0\\ 1\end{array}\right),\left(\begin{array}{c}-2\\ 3\\ 1\end{array}\right)$?

Solution

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Question 3

Question

Suppose that $S$ consists of all points in ${\mathbb{R}}^2$ that are on the x-axis or the y-axis (or both). ($S$ is called the union of the two axes.) Is $S$ a subspace of ${\mathbb{R}}^2$? Why or why not?

Solution

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