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Subtracting 4's

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Verified questions

discrete math

To prove C $\subseteq$ A $\cup$ B, we should choose an element from which set?

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question

$$ \begin{array} { l } { \text { The group } D _ { 4 } \text { acts as a group of permutations of the square regions } } \\ { \text { shown below. (The axes of symmetry are drawn for reference pur- } } \\ { \text { poses. For each square region, locate the points in the orbit of the } } \\ { \text { indicated point under } D _ { 4 } \text { . In each case, determine the stabilizer of } } \\ { \text { the indicated point. } } \end{array} $$

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algebra

Solve the equation. Check your answer using a calculator if necessary. $$ \frac{7}{12} x=\frac{3}{14}+\frac{1}{2} x $$

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linear algebra

Let $v_1$ and $v_2$ be eigenvectors of a linear operator $T$ on $R^n$, and let $\lambda_1$ and $\lambda_2$, respectively, be the corresponding eigenvalues. Prove that if $\lambda_1\neq\lambda_2$, then $\{v_1,v_2\}$ is linearly independent.

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