# 3 exercises

#### Subhotosh Khan

##### Super Moderator
Staff member
Hello can someone help me to solve these three exercises ?

https://www.scribd.com/doc/294964216/Homework-Algebra-I

I would be very happy to help me..

Thank you so much

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#### stapel

##### Super Moderator
Staff member
For those who don't want to have to do the copy-n-paste from the remote location to this thread, here's the text of the three exercises:

$$\displaystyle \mbox{Homework: January 9, 2016}$$

$$\displaystyle 1.\, \mbox{ Solve the following linear system by the Gauss method:}$$

. . . . .\displaystyle \begin{cases} \begin{align}2x\, -\, y\, +\, 3z\, +\, 4t\, &=\, 5\\4x\, -\, 2y\, +\, 5z\, +\, 6t\, &=\, 7\\6x\, -\, 3y\, +\, 7z\, +\, 8t\, &=\, 9\\\alpha x\, -\, 4y\, +\, 9z\, +\, 10t\, &=\, 11 \end{align} \end{cases}

$$\displaystyle 2.\, \mbox{ Find the eigenvalues and eigenvectors for the following matrix:}$$

. . . . .$$\displaystyle \left(\, \begin{array}{ccc}0&1&1\\1&0&1\\1&1&0\end{array}\, \right)$$

$$\displaystyle 3.\, \mbox{ Construct a table of cosets and syndromes for the }\, (9,\, 4)\mbox{-code generated by:}$$

. . . . .$$\displaystyle \, p\, =\, 1\, +\, X^2\, +\, X^4\, +\, X^5\, \in\, Z_2[X]$$

(No work is shown by the original poster at the remote location.)