Basic linear algebra

[kind lotus]

Can you show the context ?

As in, the whole page

[dim ferry]

Thank you for checking! Sadly, this was the whole slide. I expected the equations to be x1 = x1, ... , xn = xn, right? The lecturer never answered and a student told me I had to imagine a bar with zeros, but I don't see why that would make sense.

[obsidian vale]

The only way I can think is that the context was to show that nullvector is being mapped on itself to prove one condition that the identity is a linear map/transformation

[dim ferry]

Thank you! I'm sorry there's no context, why it confuses me. This was the whole page. (The second special mapping case was the transpose.) The only thing I can give is this interaction about it: Student: How did we arrive at this system of equations? Lecturer: In is the identity matrix (essentially '1' in matrix terms). If I multiple with this matrix a vector, I get the vector itself back. Student: I expected the equations to be x1 = x1, ..., xn = xn. 'Transforming' a zero vector with In (vector remains 'unmoved') leads to x1 = 0, ..., xn = 0 so I feel like I missed something here. Is my understanding incorrect? Lecturer: OK, here the representation of a system of equations and the representation of a mapping start to confuse. In maps without changing (is does not change what goes in). However if you look at it as as set of equations, it says that the variables need all be zero. Student: How was I supposed to see that all variables equal zero given In? Lecturer: In an earlier lecture we showed that a homogeneous system only has the trivial (=0) solution if the number of pivots matches the number of columns. Student: I wasn't aware of the fact that I had to imagine a bar with zeros? Thank you for your time! He never wrote back and I feel extremely stupid because I understand what he says but not why it relates.

[obsidian vale]

guess then we both feel stupid, because neither do i understand the relation

there is one more thing and that is if a matrix A is invertible then Ax = 0 has one solution => x = 0 trivially, maybe this could be the context

[dim ferry]

Haha well, that made me feel less stupid. And I think you're right, that has to be it. Thank you : )

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