diff --git a/source/linear-algebra/source/02-EV/05.ptx b/source/linear-algebra/source/02-EV/05.ptx index 8604e89d3..e4c25477b 100644 --- a/source/linear-algebra/source/02-EV/05.ptx +++ b/source/linear-algebra/source/02-EV/05.ptx @@ -489,6 +489,37 @@ Not a basis, because not only does it fail to span \IR^4, it's also linea + +

+A basis for a Euclidean vector space can be used to create alternative coordinate systems, as can +be visualized by the following tool. +

+ + + + + + + + + +

+Using the tool from , +find the unique way to write the vector +\vec v = \left[\begin{array}{c}-7\\3\end{array}\right] +as a linear combination of vectors from the basis \{\vec b_1,\vec b_2\} where +\vec b_1=\left[\begin{array}{c}-2\\2\end{array}\right] and +\vec b_2=\left[\begin{array}{c}3\\1\end{array}\right]. +

    +
  1. \vec v = 2\vec b_1-\vec b_2
    2. +
  2. \vec v = -2\vec b_1-2\vec b_2
    3. +
  3. \vec v = -\vec b_1+2\vec b_2
    4. +
  4. \vec v = \vec b_1-\vec b_2
    5. +
+

+ + + diff --git a/source/linear-algebra/source/02-EV/doenet/EV5-basis-visualization.xml b/source/linear-algebra/source/02-EV/doenet/EV5-basis-visualization.xml new file mode 100644 index 000000000..d8527d2e4 --- /dev/null +++ b/source/linear-algebra/source/02-EV/doenet/EV5-basis-visualization.xml @@ -0,0 +1,65 @@ + + + + $basisChoice.selectedIndices = 1 + (-2,-3) + + + + + (-1,3) + + + + + (4,1) + + + + + ($v.x*$b2.y-$v.y*$b2.x)/($b1.x*$b2.y-$b2.x*$b1.y) + (-$v.x*$b1.y+$v.y*$b1.x)/($b1.x*$b2.y-$b2.x*$b1.y) + + +

+ + Standard basis {e₁,e₂} + Custom basis {b₁,b₂} + +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +