LearningPython

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20 Questions

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11	Find a $4\times 4$ matrix $A$ where $A\neq I$ and $A^2 \neq I$, but $A^3 = I$.
4	How to solve / set up three equations three unknowns with a matrix?
3	Give a context-free grammar to generate the following language $L = \{ a^ib^jc^k \space\|\space 0 \leq i \leq j \leq i + k \}$
2	A linear transformation $T$ is defined by $T(x_1, x_2)$ Find the image of the line that passes through the origin and point $(1,-1)$
1	Row Reduction with Cofactor Expansion

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+5	Find a $4\times 4$ matrix $A$ where $A\neq I$ and $A^2 \neq I$, but $A^3 = I$.
+5	Row Reduction with Cofactor Expansion
+15	Give a context-free grammar to generate the following language $L = \{ a^ib^jc^k \space\|\space 0 \leq i \leq j \leq i + k \}$
+5	Let $M_{2\times 2}$ be the vector space of all $2\times 2$ matrices. Show that the set of non-singular matrices is NOT a subspace.

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0 linear-algebra × 19	0 transformation × 2
0 determinant × 4	0 geometry
0 vector-spaces × 3	0 context-free-grammar
0 matrices × 2

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