From fabb36ce7de9211d60eed07030fbf47b75784043 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Fri, 3 Oct 2025 17:04:33 +0000 Subject: [PATCH 1/7] add doenet basis visualization --- source/linear-algebra/source/02-EV/05.ptx | 26 +++++++++ .../02-EV/doenet/EV5-basis-visualization.xml | 57 +++++++++++++++++++ 2 files changed, 83 insertions(+) create mode 100644 source/linear-algebra/source/02-EV/doenet/EV5-basis-visualization.xml diff --git a/source/linear-algebra/source/02-EV/05.ptx b/source/linear-algebra/source/02-EV/05.ptx index 8604e89d3..ce0d8c978 100644 --- a/source/linear-algebra/source/02-EV/05.ptx +++ b/source/linear-algebra/source/02-EV/05.ptx @@ -489,6 +489,32 @@ 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. +Using the below tool, find the unique way to write the vector +\vec v = \left[\begin{array}{c}-7\\5\end{array}\right] +as a linear combination of vectors from the basis \{\vec b_1,\vec b_2\} where +\left[\begin{array}{c}-2\\2\end{array}\right] and +\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..6f6bca6e6 --- /dev/null +++ b/source/linear-algebra/source/02-EV/doenet/EV5-basis-visualization.xml @@ -0,0 +1,57 @@ + + + + $basisChoice.selectedIndices = 1 + (2,3) + + + + + (-2,2) + + + + + (4,1) + + + + + ($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} + +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + \ No newline at end of file From f64de61532133b701af3158f49b38a90601a6607 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Fri, 3 Oct 2025 17:10:16 +0000 Subject: [PATCH 2/7] tweaks --- source/linear-algebra/source/02-EV/05.ptx | 6 +++--- .../source/02-EV/doenet/EV5-basis-visualization.xml | 2 +- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/source/linear-algebra/source/02-EV/05.ptx b/source/linear-algebra/source/02-EV/05.ptx index ce0d8c978..34447dd9d 100644 --- a/source/linear-algebra/source/02-EV/05.ptx +++ b/source/linear-algebra/source/02-EV/05.ptx @@ -496,8 +496,8 @@ A basis for a Euclidean vector space can be used to create alternative coordinat Using the below tool, find the unique way to write the vector \vec v = \left[\begin{array}{c}-7\\5\end{array}\right] as a linear combination of vectors from the basis \{\vec b_1,\vec b_2\} where -\left[\begin{array}{c}-2\\2\end{array}\right] and -\left[\begin{array}{c}3\\-1\end{array}\right]. +\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].

@@ -505,7 +505,7 @@ as a linear combination of vectors from the basis \{\vec b_1,\vec b_2\} w

-

    +
    1. \vec v = 2\vec b_1-\vec b_2
    2. \vec v = -2\vec b_1-2\vec b_2
    3. \vec v = -\vec b_1+2\vec b_2
      4. 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 index 6f6bca6e6..35dc2d44c 100644 --- a/source/linear-algebra/source/02-EV/doenet/EV5-basis-visualization.xml +++ b/source/linear-algebra/source/02-EV/doenet/EV5-basis-visualization.xml @@ -7,7 +7,7 @@ - (-2,2) + (-1,3) From d078ede15880362cb703f8b68ae0088cf61dc7ce Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Fri, 3 Oct 2025 17:27:17 +0000 Subject: [PATCH 3/7] tweak interactive --- .../02-EV/doenet/EV5-basis-visualization.xml | 24 +++++++++---------- 1 file changed, 11 insertions(+), 13 deletions(-) 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 index 35dc2d44c..1ba4286d3 100644 --- a/source/linear-algebra/source/02-EV/doenet/EV5-basis-visualization.xml +++ b/source/linear-algebra/source/02-EV/doenet/EV5-basis-visualization.xml @@ -30,21 +30,18 @@ - - - - - - - - - - + + - - + + + + + + + @@ -54,4 +51,5 @@ - \ No newline at end of file + + \ No newline at end of file From 768a4e7ae9b7026d0d3811b30b4b7ff58098e507 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Fri, 3 Oct 2025 17:33:45 +0000 Subject: [PATCH 4/7] and another tweak --- source/linear-algebra/source/02-EV/05.ptx | 4 ++-- .../source/02-EV/doenet/EV5-basis-visualization.xml | 3 ++- 2 files changed, 4 insertions(+), 3 deletions(-) diff --git a/source/linear-algebra/source/02-EV/05.ptx b/source/linear-algebra/source/02-EV/05.ptx index 34447dd9d..fa7a4431f 100644 --- a/source/linear-algebra/source/02-EV/05.ptx +++ b/source/linear-algebra/source/02-EV/05.ptx @@ -494,10 +494,10 @@ 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. Using the below tool, find the unique way to write the vector -\vec v = \left[\begin{array}{c}-7\\5\end{array}\right] +\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]. +\vec b_2=\left[\begin{array}{c}3\\1\end{array}\right].

      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 index 1ba4286d3..3677e3234 100644 --- a/source/linear-algebra/source/02-EV/doenet/EV5-basis-visualization.xml +++ b/source/linear-algebra/source/02-EV/doenet/EV5-basis-visualization.xml @@ -40,6 +40,8 @@       + + @@ -52,4 +54,3 @@       - \ No newline at end of file From 59b5c60b76cfa96d41d33255947af0e080d91e04 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Fri, 3 Oct 2025 15:39:03 -0500 Subject: [PATCH 5/7] update doenet interactive --- .../02-EV/doenet/EV5-basis-visualization.xml | 63 +++++++++++-------- 1 file changed, 36 insertions(+), 27 deletions(-) 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 index 3677e3234..d8527d2e4 100644 --- a/source/linear-algebra/source/02-EV/doenet/EV5-basis-visualization.xml +++ b/source/linear-algebra/source/02-EV/doenet/EV5-basis-visualization.xml @@ -2,7 +2,7 @@ $basisChoice.selectedIndices = 1 - (2,3) + (-2,-3) @@ -28,29 +28,38 @@

      - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + From 8872c7d90d037ffead1e8ecf8df401fc145830e3 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Fri, 3 Oct 2025 15:42:57 -0500 Subject: [PATCH 6/7] separate tool and activity --- source/linear-algebra/source/02-EV/05.ptx | 23 ++++++++++++++--------- 1 file changed, 14 insertions(+), 9 deletions(-) diff --git a/source/linear-algebra/source/02-EV/05.ptx b/source/linear-algebra/source/02-EV/05.ptx index fa7a4431f..8fe841ba4 100644 --- a/source/linear-algebra/source/02-EV/05.ptx +++ b/source/linear-algebra/source/02-EV/05.ptx @@ -489,22 +489,27 @@ 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. +

      + + + + + +       +

      -A basis for a Euclidean vector space can be used to create alternative coordinate systems. -Using the below tool, find the unique way to write the vector +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. \vec v = -2\vec b_1-2\vec b_2
        3. From 174f9647e67053cd0e99e416bdf558d87114d7f7 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Fri, 3 Oct 2025 15:46:48 -0500 Subject: [PATCH 7/7] fix xref --- source/linear-algebra/source/02-EV/05.ptx | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/source/linear-algebra/source/02-EV/05.ptx b/source/linear-algebra/source/02-EV/05.ptx index 8fe841ba4..e4c25477b 100644 --- a/source/linear-algebra/source/02-EV/05.ptx +++ b/source/linear-algebra/source/02-EV/05.ptx @@ -504,7 +504,7 @@ be visualized by the following tool.

        -Using the tool from , +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