Confusion with how to make an augmented matrix

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The discussion centers on confusion regarding the representation of a linear system in augmented matrix form. A participant questions the absence of the constant "4" in the first equation of the matrix. Other contributors confirm that the "4" is likely a misprint and that the correct representation should include it. This clarification reassures the original poster, alleviating their concerns about the accuracy of their understanding. The conversation highlights the importance of verifying details in mathematical representations.
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Homework Statement


So in the attachment you'll see a picture taken from a linear algebra book where a linear system of equations is presented in the equivalent augmented matrix form. I'm confused about the representation of the first equation in the augmented matrix. What happened to the constant 4? Shouldn't the first row in the matrix be [ 0 -1 -1 1 | -4 ]?

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John004 said:
Shouldn't the first row in the matrix be [ 0 -1 -1 1 | -4 ]?

Yes, it should be. The "4" in the first equation is probably a misprint.
 
Stephen Tashi said:
Yes, it should be. The "4" in the first equation is probably a misprint.
Ah ok, good. I thought I was going crazy for a second there.
 

Thread 'Find the polar form of a complex number'

The working out suggests first equating ## \sqrt{i} = x + iy ## and suggests that squaring and equating real and imaginary parts of both sides results in ## \sqrt{i} = \pm (1+i)/ \sqrt{2} ## Squaring both sides results in: $$ i = (x + iy)^2 $$ $$ i = x^2 + 2ixy -y^2 $$ equating real parts gives $$ x^2 - y^2 = 0 $$ $$ (x+y)(x-y) = 0 $$ $$ x = \pm y $$ equating imaginary parts gives: $$ i = 2ixy $$ $$ 2xy = 1 $$ I'm not really sure how to proceed from here.
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