Voyska
Reputation
7,523
Next privilege 10,000 Rep.
Access moderator tools
 Mar 12 comment If $A,B\in M_2(\mathbb{R})$, show that $(AB-BA)(AB-BA)$ is a scalar matrix. @MichaelBiro No. The book I'm using still didn't introduce it. So I suppose it can't be used (I usually answer the books trying to using only what is given, I guess the authors expect that from the students) - But I'll look for it because I'm curious. Thanks! Mar 12 asked If $A,B\in M_2(\mathbb{R})$, show that $(AB-BA)(AB-BA)$ is a scalar matrix. Mar 11 awarded Popular Question Mar 10 asked If $A,B$ are invertible, show that $AB$ is invertible and express $(AB)^{-1}$ in terms of $A^{-1},B^{-1}$. Mar 8 accepted When is an upper triangular matrix invertible? Mar 8 comment When is an upper triangular matrix invertible? Very good. That was one of the possible ways I was thinking about. Mar 8 comment When is an upper triangular matrix invertible? Please, see my reply to John Wayland. Mar 8 comment When is an upper triangular matrix invertible? Please, see my reply to John Wayland. Mar 8 comment When is an upper triangular matrix invertible? @JohnWaylandBales Yes, but I'm trying to do without the notion of determinant which wasn't introduced in the book yet. But perhaps, solving the exercise means exactly developing the determinant. Mar 8 asked When is an upper triangular matrix invertible? Mar 3 awarded Nice Answer Feb 26 awarded Yearling Feb 26 asked If $a>0$, then $b<0 \implies ab < 0$? Feb 13 awarded Favorite Question Feb 13 comment How do I prove that sine is dependent only on the angle? @YvesDaoust Yes. Sine has two meanings, it is the single function argument and It is also the ratio of two sides of the right triangle (opposite/hypotenuse). As this ratio depends only on the angle, one can simplify things and get $h=1$ and hence: $opposite/1=opposite$. (I guess this is correct). Feb 13 comment How do I prove that sine is dependent only on the angle? @YvesDaoust I'm talking about this definition. Feb 13 comment How do I prove that sine is dependent only on the angle? @YvesDaoust Yes, I know. But I'm talking about that definition. Feb 13 comment How do I prove that sine is dependent only on the angle? @YvesDaoust Uh? Feb 13 comment How do I prove that sine is dependent only on the angle? @GiovanniResta Is there a remedy to this? For example, adding it to the hypotenuse? Feb 13 asked How do I prove that sine is dependent only on the angle?