System of Linear Equations: a & b Values

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Homework Statement



For the following system, indicate for what values of a and b the system will have
i.) One Solution
ii.) No Solutions
iii.) Infinitely Many Solutions

Homework Equations


2x + y - az = 1
5x + 3y - 2az = 2+2b
x + y + az = b

The Attempt at a Solution



[ 1 0 -2a | 1-b ]
[ 0 1 2a | 3b-1 ]
[ 0 0 a | -b ]

Every time I row reduce the system I end up with a row echelon form that leaves me with no means to decipher a and b. Making me think I'm doing something wrong.

Thanks.
 
Last edited:
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I think you'll need to show use what you got for the row echelon reduction before anyone can comment.
 


Yeah I just put it in the original post.

Thank you for the heads up.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

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