Question

Can a curve be expressed in matrix form? e.g. ax^2+bxy+cy^2
Can a curve be expressed in matrix form? e.g. ax^2+bxy+cy^2
@Mathematics

Answer 1

do u mean like?: \[\left[\begin{matrix}a & b & c\\ d & e & f\end{matrix}\right]\left[\begin{matrix}x^{2} \\ xy \\ y^{2}\end{matrix}\right] = \left[\begin{matrix}ax^{2} + bxy + cy^{2} \\ dx^{2} +exy + fy^{2} \end{matrix}\right]\]

Answer 2

yh. Can the final answer be in a single line?

Answer 3

yea you can do a matrix multiplication with a 1x3 matrix and a 3x1 matrix

Answer 4

although matrix is used for multiple lines mostly

Answer 5

my teacher gave me something like \[\left[\begin{matrix}x & y \end{matrix}\right]\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]\left[\begin{matrix}x \\ y\end{matrix}\right]\] = \[ax^2 +(b+c)xy+ dy^2\]

Answer 6

so doing matrix mutiplication for this u would do \[(x \times a \times x) + (x \times c \times y) + (y \times b \times x) + (y \times d \times y)\]

Answer 7

So...can I do differentiation operations on the matrix?

Answer 8

yes, operations act differently between scalars and matrices

Answer 9

for matrix calculus you need to find eigen vectors and eigen values

Answer 10

I'll read on them. Thanks for everything!