# Linearly Independent (Matrix), help!

• May 19th 2006, 05:14 AM
orange890
Linearly Independent (Matrix), help!
Linearly independent (MAtrix)

--------------------------------------------------------------------------------

The rows of the matrix:
Show it is linearly independent

1 4 -2 3
2 -2 1 1
3 1 2 11

I have the solution, but I don't understand.

Solution:

a(1 4 -2 3) + b(2 -2 1 1 ) + c(3 1 2 11) = (0 0 0 0)

/\
|
\/
why the above equation can change to the below equations??????

a + 2b + 3c = 0
4a - 2b + c = 0
-2a + b + 2 c = 0
3a + b + 11c = 0

a=b=c=0, so it is linearly independent.

Confused :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused: :confused:
• May 19th 2006, 05:32 AM
CaptainBlack
Quote:

Originally Posted by orange890
Linearly independent (MAtrix)

--------------------------------------------------------------------------------

The rows of the matrix:

1 4 -2 3
2 -2 1 1
3 1 2 11

I have the solution, but I don't understand.

You want to show that the rows of this matrix are linearly independent?

If they are linearly independent the only solution of:

Quote:

a(1 4 -2 3) + b(2 -2 1 1 ) + c(3 1 2 11) = (0 0 0 0)

is the trivial solution a=b=c=0.

Quote:

a + 2b + 3c = 0
4a - 2b + c = 0
-2a + b + 2 c = 0
3a + b + 11c = 0
This is just your previous vector equation written as four scalar equations,
which you should proceed to solve to show that you must have: a=b=c=0,
and so you can conclude that the rows are linearly independent.

RonL
• May 19th 2006, 05:35 AM
orange890
a(1 4 -2 3) + b(2 -2 1 1 ) + c(3 1 2 11) = (0 0 0 0)
[COLOR=DarkOrange]
/\
|
\/
How does it form??????

a + 2b + 3c = 0
4a - 2b + c = 0
-2a + b + 2 c = 0
3a + b + 11c = 0
• May 19th 2006, 06:28 AM
CaptainBlack
Quote:

Originally Posted by orange890
a(1 4 -2 3) + b(2 -2 1 1 ) + c(3 1 2 11) = (0 0 0 0)
[COLOR=DarkOrange]

Look at the first component of the expressions on the Left and Right hand sides:

a + 2 b +3 c = 0

Now the seecond component:

4a-2b+c=0

Third component:

-2a+b+2c=0

Fourth component:

3a+b+11c=0

RonL
• May 19th 2006, 06:42 AM
orange890
hi RonL,

yeah really thanks for your helping. :p