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Are the following two systems of linear equations equivalent (2)


Solution to Linear Algebra Hoffman & Kunze Chapter 1.2 Exercise 1.2.3

Solution: Yes the two systems are equivalent. We show this by writing each equation of the first system in terms of the second, and conversely.
x1x3=34(x1+x2+4x3)+14(x1+3x3+8x3)x2+3x3=14(x1+x2+4x3)+14(x1+3x3+8x3)
and
x1+x2+4x3=(x1x3)+(x2+3x3)x1+3x2+8x3=(x1x3)+3(x2+3x3)12x1+x2+52x3=12(x1x3)+(x2+3x3)


Linearity

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