(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the rank of the matrix A,where

[tex]A= \left(

\begin{array}{cccc}

1 & 1 & 2 & 3\\

4 & 3 & 5 & 16\\

6 & 6 & 13 & 13\\

14 & 12 & 23 & 45

\end{array}

\right)

[/tex]

Find vectors[tex]x_0[/tex]and[tex]e[/tex] such that any solution of the equation

[tex]Ax= \left(

\begin{array}{c}

0\\

2\\

-1\\

3

\end{array}

\right)

[/tex] [tex](*)[/tex]

can be expressed in the form [tex]x_0+\lambdae[/tex] where [tex]\lambda\epsilonR[/tex]

Hence show that there is no vector which satisfies [tex]*[/tex] and has all its elements positive

2. Relevant equations

First attempt at such a question, so unknown are any relevant equations

3. The attempt at a solution

Well for the first part to get the rank I put A in RRE form and then counted the number of non-zero rows and got for so [tex]r(A)=4[/tex]

now for the second part,I thought to solve the equation by multiplying by [tex]A^{-1}[/tex] and finding [tex]x[/tex] but then I realized that I have no idea where to get [tex]x_0[/tex] or [tex]\lambda[/tex] or [tex]e[/tex]

can anyone show me how to do these types of questions or can show me some similar example?

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# Homework Help: Rank of a matrix and more

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