Question

easy question on eigen vectors and values

Answer 1

\(\lambda_{1,...}\)

Answer 2

why isn’t (2-landa * I) applied to the two 2s in matrix A?It is applied to -5 and -2.

Answer 3

because you subtract identity matrix. where all elements off the diagonal are zeros.
so 2-0=2

Answer 4

\[\textbf I_1=(1)\]
\[\textbf I_2=\begin{pmatrix}\ 1 & 0\\0&1 \end{pmatrix}\]
\[\textbf I_3=\begin{pmatrix}\ 1 & 0&0\\0&1&0\\0&0&1 \end{pmatrix}\]

\[\lambda\textbf I_1=(\lambda)\]
\[\lambda\textbf I_2=\begin{pmatrix}\ \lambda & 0\\0&\lambda \end{pmatrix}\]
\[\lambda\textbf I_3=\begin{pmatrix}\ \lambda & 0&0\\0&\lambda&0\\0&0&\lambda \end{pmatrix}\]

Answer 5

oh crap i forgot about the identity matrix

Answer 6

who wants the medal?

Answer 7

\[(\textbf A-\lambda\textbf I)=\begin{pmatrix}\ a_{11} & a_{12}\\a_{21}&a_{22} \end{pmatrix} -\begin{pmatrix}\ \lambda & 0\\0&\lambda \end{pmatrix}\]\[\qquad =\begin{pmatrix}\ a_{11}-\lambda & a_{12}\\a_{21}&a_{22}-\lambda \end{pmatrix} \]

Answer 8

uncle rhaukus did the most typing by far lol thanks

Answer 9

and all within six minutes

Answer 10

heh i just did it on photoshop

Answer 11

2 lazy to type the matix built-in code

Answer 12

*matrix