Question

http://prntscr.com/4xdy20

Need some help understanding this. Thanks

Answer 1

@hartnn
@amistre64

Answer 2

those
C [1 3 ]' = [2 2]'
and all are matrix multiplication equations,
but i have no idea about that diagrams! :O

Answer 3

\[\left[\begin{matrix}1/2 & 1/2 \\1/2 & 1/2\end{matrix}\right]\left[\begin{matrix}1 \\ 3\end{matrix}\right] = \left[\begin{matrix} \frac{ 1 }{ 2} 1 +\frac{ 1 }{ 2}3 \\ \frac{ 1 }{ 2}1+\frac{ 1 }{ 2}3 \end{matrix}\right]=\left[\begin{matrix}2 \\2\end{matrix}\right]\]

Answer 4

\[\left[\begin{matrix}1/2 & 1/2 \\1/2 & 1/2\end{matrix}\right]\left[\begin{matrix}-1 \\ 1\end{matrix}\right] = \left[\begin{matrix} \frac{ 1 }{ 2} \times -1 +\frac{ 1 }{ 2}1 \\ \frac{ 1 }{ 2} \times -1+\frac{ 1 }{ 2}1 \end{matrix}\right]=\left[\begin{matrix}0 \\0\end{matrix}\right]\]

Answer 5

ohh so the matrix is being multiplied

Answer 6

Yes
then the vectors are shown in the diagram
If you show the original and the anwer vectors after multiplication, you can see what this matrix multiplication does to the original vector

Answer 7

what exactly does the matrix multiplication do to the vectors?

Answer 8

matirx multiplication on a vector this way gives a linear transformation of the vector
a linear transformation being a combination of a reflection, rotation and a scaling

Answer 9

so how do i know which transformation is taking place

Answer 10

by carrying out the multiplication to a few vectors, and put them in a diagram
and see what has happened

Answer 11

http://prntscr.com/4xene2

@abtster can you explain this to me please

Answer 12

you can also try to see if you can create a combination of matrixes that when multiplied give your matrix
see
http://en.wikipedia.org/wiki/Linear_map#Examples_of_linear_transformation_matrices

Answer 13

E = CD
1/2 * 2 + 1/2 * 0 = 1
1/2 * 2 + 1/2 * 0 = 1
1/2 * 0 + 1/2 * 1 = 1/2
1/2 * 0 + 1/2 * 1 = 1/2
so
\[E = \left[\begin{matrix}1 & 1/2 \\ 1 & 1/2\end{matrix}\right]\]

Answer 14

C[v] and after that D[v] gives the same resulting vector as E[v}

http://en.wikipedia.org/wiki/Matrix_multiplication#Linear_transformations
explains how it is done and a lot more more on matrixes