Place the cursor over the image to start the animation.
The origin $\displaystyle \begin{bmatrix}0 \\ 0 \\0\end{bmatrix}$ of the color cube is at Black,
the head of $\displaystyle \begin{bmatrix}1 \\ 0 \\0\end{bmatrix}$ is at Red,
the head of $\displaystyle \begin{bmatrix}0 \\ 1 \\0\end{bmatrix}$ is at Green and
the head of $\displaystyle \begin{bmatrix}0 \\ 0 \\1\end{bmatrix}$ is at Blue.
Place the cursor over the image to start the animation.
Place the cursor over the image to start the animation.
Since Teal and Yellow are the heads of particular vectors in the Color Cube, to construct a transition I connected the heads with a line segment. Points on this line segment are the heads of special linear combinations of the vectors representing Teal and Yellow. As an exercise write the linear combinations which are used in the above transition.
Place the cursor over the image to start the animation.
In the above animation I used the colors from the line segment connecting Teal and Yellow to color the rectangles in the middle of the square.
Here is the unit circle colored using colors from the line segment connecting Teal and Yellow.
A nonzero matrix is said to be in row echelon form if its first row is a nonzero row and each nonzero row bellow the first has strictly more leading zeros then the previous row.
A nonzero matrix which is in row echelon form is said to be in reduced row echelon form if the leading entries off all nonzero rows are equal to 1 and this 1 is the only nonzero entry in its column.