- #1

karush

Gold Member

MHB

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$\tiny{45.4.T40}$

Suppose that the coefficient matrix of a consistent system of linear equations has two columns that are identical. Prove that the system has infinitely many solutions. Refer to the DTSLS Diagram

\item using augmented matrix A for example with c1 and c3 identical

$\left[

\begin{array}{rrr|r}

1&4&1&12\\

2&3&2&14\\

3&2&3&16

\end{array}\right]$

eMH returned the following RREF which show c1 and c3 as pivot columns

this is a violation of RREF

$\text{REFF}(A)=\left[ \begin{array}{rrr|r}

1 & 0 & 1 & 4 \\

0 & 1 & 0 & 2 \\

0 & 0 & 0 & 0

\end{array} \right]$

the matrix was dirived from the the possible set of $x_1=1\ x_2=2\ x_3=3$

a little perplexed as to whar we need to do when one row is all zero's after RREF

also as a result of RREF can this be just an 2x4 augmented matrix, r<n

this is supposed to be a proof which I am not good at

here is the DTSLS Diagram we are supposed to us

Suppose that the coefficient matrix of a consistent system of linear equations has two columns that are identical. Prove that the system has infinitely many solutions. Refer to the DTSLS Diagram

\item using augmented matrix A for example with c1 and c3 identical

$\left[

\begin{array}{rrr|r}

1&4&1&12\\

2&3&2&14\\

3&2&3&16

\end{array}\right]$

eMH returned the following RREF which show c1 and c3 as pivot columns

this is a violation of RREF

$\text{REFF}(A)=\left[ \begin{array}{rrr|r}

1 & 0 & 1 & 4 \\

0 & 1 & 0 & 2 \\

0 & 0 & 0 & 0

\end{array} \right]$

the matrix was dirived from the the possible set of $x_1=1\ x_2=2\ x_3=3$

a little perplexed as to whar we need to do when one row is all zero's after RREF

also as a result of RREF can this be just an 2x4 augmented matrix, r<n

this is supposed to be a proof which I am not good at

here is the DTSLS Diagram we are supposed to us

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