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1 Participation
- Unmute yourself
2 Homework Review
- From homework 20math530retReadingTheTextbook
2.1 Is Dot Product Nice?
- Nice = group properties
- They aren't because its not closed
- However, we still like dot product because it can easily tell us if the thing is perpendicular
2.2 Inverse of a matrix
- Use 2 systems of equations (2 variables, 2 equations, twice) KBe20math530srcMatrixInverse.png
- \(y = \frac{c}{bc-ad} = \frac{-c}{ad-bc}\)
- Determinant determines whether its possible to have an inverse
(because if it's zero, then it's not possible!)
- A matrix with no inverse is SINGULAR
- Determinant of \(A\) is zero
- A has no inverse
- invertable matrix theorem
3 Proof Attempt Discussion Page?
4 Small Groups
- Calculate cross products
- Graph cross products
- Cross Product geometry?
- It's the perpendicular!
- #bonushw its perpendicular
- Determinant geometric interpretation?
- It's the perpendicular! IF you crossproduct-ify
- \(\begin{bmatrix}x\\y\end{bmatrix}\Rightarrow\left|\begin{bmatrix}i&j\\x&y\end{bmatrix}\right| = iy-jx = \begin{bmatrix}y\\-x\end{bmatrix}\)
## Taking the Determinant (why
--?)
- We take the sub-matrices on a torus
- But if you wrap everything around properly then you have a plus in front of every coefficient
- But if you don't wrap it, then the determinant ends up being the negative, so that's why there's the whole plus minus thing.