MTH1004 Linear Algebra Tutorial Class 6

Question 1

Question

If $A$ and $B$ are $n\times n$ matrices of rank $n$, prove that the matrix $AB$ has rank $n$ (hint: use the fact that $A$ and $B$ are invertible).

Solution

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Question 2

Question

Show that the set $S=\{x\in {\mathbb{R}}^3:x_1\le 0\text{ and }{x}_2\ge 0\}$ is not a vector space by showing that at least one of the vector space axioms is not satisfied.

Solution

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Question 3

Question

Show that the set of all upper triangular $2\times 2$ matrices is a vector space.

Solution

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