- #1
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Homework Statement
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
Homework Equations
First attempt at such a question, so unknown are any relevant equations
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?