Applied Linear Algebra Question, I'm posting question give me one second

- anonymous

Applied Linear Algebra Question, I'm posting question give me one second

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- anonymous

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- anonymous

okay so I got to the point where I dont know what to do next

- anonymous

I have to find values of "a" where the system has no solution, Unique Solution, and infinte solutions

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- anonymous

I got the system to row echelon form

- anonymous

lt me draw what i got out

- anonymous

|dw:1442684208867:dw|

- anonymous

Do I need to put this into reduce echelon form?

- anonymous

Actually yea I think that would help

- anonymous

let me do that on paper, first brb

- anonymous

oh wait made a mistake in the drawing, the "3a+10" has a denominator of "2a-4"

- anonymous

|dw:1442685001288:dw|

- anonymous

If a is not equal to 2, then we have a unique solution
Plugging in a = 2 in the second we get
1 -2 3 3
0 -4+2a 3-3a 10-3a
0 0 1 -1
the middle row second term is non zero, so you can solve for it, and that produces a triangular system with a unique solution. Try a number.

- IrishBoy123

find the determinant and set it to zero and that might save a lot of typing

- IrishBoy123

ie set to zero and solve for a

- anonymous

I assume you mean the determinant of the coefficient matrix.

- anonymous

the determinant of the coefficient matrix is
12 - 6a
the matrix has a unique solution as long as the determinant is non zero.
12 - 6a = 0
12 = 6a
12/6 = a
if a â‰ 2 then the system has a unique solution (because the determinant is non-zero)

- anonymous

if a = 2 you have a contradiction, can you see why?

- anonymous

Case 1: "a" does not equal to 2, give a uniqure solution
case 2: "a" equals 2, gives no Solution
Case 3: there is never a infinite solution
is that correct?

- IrishBoy123

yeah, work that way :p
if \(a \ne 2\) you have a solution
so set a to 2 and do your reduction, see where you go

- anonymous

It will be no solution if u get set a = 2

- anonymous

correct

- anonymous

So would it be right to say that this system does not have infinite solutions?

- anonymous

So it has no solution when a=2, a unique solution a does not =2, but not infinite solutions right? or when a does not equal to 2 it will have infinite solution as well?

- anonymous

anyone there?

- anonymous

it will never have infinite solutions

- anonymous

what I'm confused about is that if a does not equal to 2, will it have infinite solutions

- anonymous

oh ok, can you tell me why though?

- anonymous

if a does not equal to 2 it will have a unique solution
if a is equal to 2 it will have no solution (because of contradiction)
there is no case of 'infinite solutions'

- anonymous

oooh I see, lol thanks, I blanked out for a second there. Thank you so much!

- anonymous

Your welcome.

- IrishBoy123

|dw:1442690538127:dw|

- IrishBoy123

|dw:1442690850922:dw|

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