I have been doing some practice questions for university, and one of them is regarding row reducing a complex matrix. From what I can work out, I think (i could very well be wrong) that the first unknown (row 1) should be (1/32)(41i - 82) And as such, the second unknown should be (-3-2i) - (2 + 2i)((1/32)(41i - 82))
However this looks messy, and is making me think i may have done it wrong.
If someone could please let me know if i am correct or not, and if not, where i went wrong, i would be hugely grateful.
Thanks heaps in advance Corey
The trick here is to multiply be the conjugate, giving: $$\frac{-3+14i}{4-5i}$$ $$\frac{-3+14i}{4-5i} = \frac{-3+14i}{4-5i}\cdot \frac{4+5i}{4+5i} = \frac{-82+41i}{41}=-2+i$$ Thus the second element of the second row now reads: $$(-3-2i)- (2+2i)(-2+i)=3$$