# Rank, and Row Multiple Examples

• February 20th 2011, 06:59 AM
situation
Rank, and Row Multiple Examples
is it possible to have a system satifying this:
A system of four equations in three variables such that the associated coecient matrix has no zero

entries, no row is a multiple of any other row, and the matrix has rank 2?

i thought that if no row is a multiple of any other than how could u get anything other than rank 3??

I also need to somehow come up with examples of:

A system of three equations in four variables such that the associated coeffcient matrix has no zero
entries, no row is a multiple of any other row, and the matrix has rank 2.

A system of three equations in four variables such that the associated coefficient matrix has no zero entries
and has rank 3.

not sure what examples satify the above but any help would be much appreciated as this is all very new to me.

cheers

• February 20th 2011, 08:44 AM
alexmahone
Quote:

Originally Posted by situation
is it possible to have a system satifying this:
A system of four equations in three variables such that the associated coecient matrix has no zero

entries, no row is a multiple of any other row, and the matrix has rank 2?

i thought that if no row is a multiple of any other than how could u get anything other than rank 3??

I also need to somehow come up with examples of:

A system of three equations in four variables such that the associated coeffcient matrix has no zero
entries, no row is a multiple of any other row, and the matrix has rank 2.

A system of three equations in four variables such that the associated coefficient matrix has no zero entries
and has rank 3.

not sure what examples satify the above but any help would be much appreciated as this is all very new to me.

cheers

1) $A=\left[ \begin{array}{cccc} 1 & 2 & 3 \\ 5 & 6 & 7 \\ 6 & 8 & 10 \\ 7 & 10 & 13 \end{array} \right]$

(R3=R1+R2, R4=2R1+R2)

Try 2) and 3) yourself.
• February 20th 2011, 10:12 AM
situation
Quote:

Originally Posted by alexmahone
1) $A=\left[ \begin{array}{cccc} 1 & 2 & 3 \\ 5 & 6 & 7 \\ 6 & 8 & 10 \\ 7 & 10 & 13 \end{array} \right]$

(R3=R1+R2, R4=2R1+R2)

Try 2) and 3) yourself.

ok thanks for that. for part 2 i get $B=\left[ \begin{array}{cccc} 1 & 2 & 3 & 5 \\ 6 & 7 & 8 & 9 \\ 7 & 9 & 11 & 14 \end{array} \right]$

is that correct??
• February 20th 2011, 12:23 PM
alexmahone
Quote:

Originally Posted by situation
ok thanks for that. for part 2 i get $B=\left[ \begin{array}{cccc} 1 & 2 & 3 & 5 \\ 6 & 7 & 8 & 9 \\ 7 & 9 & 11 & 14 \end{array} \right]$

is that correct??

Yes.