From 9c5c510676dacd0f93a5c10047895379906e9e04 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Sun, 20 Apr 2025 16:19:24 -0500 Subject: [PATCH 1/9] AT2 tweak to emphasize transformed basis vectors --- .../exercises/outcomes/AT/AT2/generator.sage | 4 +- .../exercises/outcomes/AT/AT2/template.xml | 87 ++++++++++++++----- 2 files changed, 69 insertions(+), 22 deletions(-) diff --git a/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage b/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage index df21f8cf7..8452c83a8 100644 --- a/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage +++ b/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage @@ -35,10 +35,12 @@ class Generator(BaseGenerator): "varmap": A*xs, "varvector": xs, "Sstandardmatrix": A, + "Scols": [{"i": i+1, "col": A.col(i)}], "Trows": Trows, "Tcols": Tcolumns, "Tstandardmatrix": B, "vector": v, - "Tvector": B*v + "Tvector": B*v, + "Tcols": [{"i": i+1, "col": B.col(i)}], } diff --git a/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml b/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml index 917ec0e61..a3b13d6d5 100644 --- a/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml +++ b/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml @@ -1,28 +1,73 @@ - -

Explain and demonstrate how to compute - the standard matrix for the linear transformation - S:\mathbb{R}^{{Scols}} \to \mathbb{R}^{{Srows}} given by - S\left( {{varvector}} \right) = {{varmap}} - by computing transformations of the standard basic vectors.

- - -

{{Sstandardmatrix}}

- + +

+Consider the linear transformation +S:\mathbb{R}^{{Scols}} \to \mathbb{R}^{{Srows}} given by +S\left( {{varvector}} \right) = {{varmap}}. +

+ + + +

+Compute the transformation of each vector from the standard +basis for \mathbb R^{{Scols}}. +

+ + +

+ +S(\vec e_{ {{i}} }) = {{col}} + +

+ + + + +

+Explain and demonstrate how these are used to +form the standard matrix for this transformation. +

+ + +

{{Sstandardmatrix}}

+ + - -

Let T:\mathbb{R}^{{Tcols}} \to \mathbb{R}^{{Trows}} - be the linear transformation given by the standard matrix - {{Tstandardmatrix}}. - Explain and demonstrate how to compute - T\left({{vector}}\right) by using the values of - transformed standard basic vectors.

- - -

T\left({{vector}}\right)={{Tvector}}

- + +

+Consider the linear transformation +T:\mathbb{R}^{{Tcols}} \to \mathbb{R}^{{Trows}} +defined by the standard matrix {{Tstandardmatrix}}. +

+ + + +

+Describe how this map transforms each of the vectors for the +standard basis of \mathbb R^{{Tcols}}. +

+ + +

+ +T(\vec e_{ {{i}} }) = {{col}} + +

+ + + + +

+Explain and demonstrate how to use these to compute +T\left({{vector}}\right). +

+ + +

T\left({{vector}}\right)={{Tvector}}

+ + From 8a21e1f2b456a9a8b978f387ab95e8f74ff7cc72 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Sun, 20 Apr 2025 16:27:31 -0500 Subject: [PATCH 2/9] Update template.xml --- .../linear-algebra/exercises/outcomes/AT/AT2/template.xml | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml b/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml index a3b13d6d5..eeec15d7e 100644 --- a/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml +++ b/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml @@ -1,13 +1,13 @@ - +

Consider the linear transformation S:\mathbb{R}^{{Scols}} \to \mathbb{R}^{{Srows}} given by S\left( {{varvector}} \right) = {{varmap}}.

- +

@@ -36,13 +36,13 @@ form the standard matrix for this transformation. - +

Consider the linear transformation T:\mathbb{R}^{{Tcols}} \to \mathbb{R}^{{Trows}} defined by the standard matrix {{Tstandardmatrix}}.

- +

From 6182257ce3b9d440d34ef564e767588a96e803b0 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Sun, 20 Apr 2025 16:32:18 -0500 Subject: [PATCH 3/9] Update template.xml --- .../exercises/outcomes/AT/AT2/template.xml | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml b/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml index eeec15d7e..db70a4630 100644 --- a/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml +++ b/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml @@ -8,7 +8,7 @@ Consider the linear transformation S\left( {{varvector}} \right) = {{varmap}}.

- +

Compute the transformation of each vector from the standard @@ -22,8 +22,8 @@ S(\vec e_{ {{i}} }) = {{col}}

- - + +

Explain and demonstrate how these are used to @@ -33,7 +33,7 @@ form the standard matrix for this transformation.

{{Sstandardmatrix}}

- + @@ -43,7 +43,7 @@ Consider the linear transformation defined by the standard matrix {{Tstandardmatrix}}.

- +

Describe how this map transforms each of the vectors for the @@ -57,8 +57,8 @@ T(\vec e_{ {{i}} }) = {{col}}

- - + +

Explain and demonstrate how to use these to compute @@ -68,6 +68,6 @@ Explain and demonstrate how to use these to compute

T\left({{vector}}\right)={{Tvector}}

- + From ea51bd7882fde0680d3e8e747dee44b4adec03d7 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Sun, 20 Apr 2025 16:40:59 -0500 Subject: [PATCH 4/9] Update generator.sage --- .../linear-algebra/exercises/outcomes/AT/AT2/generator.sage | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage b/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage index 8452c83a8..6682b5d34 100644 --- a/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage +++ b/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage @@ -35,12 +35,12 @@ class Generator(BaseGenerator): "varmap": A*xs, "varvector": xs, "Sstandardmatrix": A, - "Scols": [{"i": i+1, "col": A.col(i)}], + "Scols": [{"i": i+1, "col": A.column(i)}], "Trows": Trows, "Tcols": Tcolumns, "Tstandardmatrix": B, "vector": v, "Tvector": B*v, - "Tcols": [{"i": i+1, "col": B.col(i)}], + "Tcols": [{"i": i+1, "col": B.column(i)}], } From d9c8dda96a28e696c92922cb24c755514600059a Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Sun, 20 Apr 2025 16:52:54 -0500 Subject: [PATCH 5/9] why am i coding without a codespace? --- .../linear-algebra/exercises/outcomes/AT/AT2/generator.sage | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage b/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage index 6682b5d34..bdfc0d784 100644 --- a/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage +++ b/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage @@ -35,12 +35,12 @@ class Generator(BaseGenerator): "varmap": A*xs, "varvector": xs, "Sstandardmatrix": A, - "Scols": [{"i": i+1, "col": A.column(i)}], + "Scols": [{"i": i+1, "col": A.column(i)} for i in range(Scolumns)], "Trows": Trows, "Tcols": Tcolumns, "Tstandardmatrix": B, "vector": v, "Tvector": B*v, - "Tcols": [{"i": i+1, "col": B.column(i)}], + "Tcols": [{"i": i+1, "col": B.column(i)} for i in range(Tcolumns)], } From b80b3a2a7414558f80bc196f1881a4644109b042 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Sun, 20 Apr 2025 16:58:35 -0500 Subject: [PATCH 6/9] Update generator.sage --- .../linear-algebra/exercises/outcomes/AT/AT2/generator.sage | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage b/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage index bdfc0d784..4770e9419 100644 --- a/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage +++ b/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage @@ -35,12 +35,12 @@ class Generator(BaseGenerator): "varmap": A*xs, "varvector": xs, "Sstandardmatrix": A, - "Scols": [{"i": i+1, "col": A.column(i)} for i in range(Scolumns)], + "Scolumns": [{"i": i+1, "col": A.column(i)} for i in range(Scolumns)], "Trows": Trows, "Tcols": Tcolumns, "Tstandardmatrix": B, "vector": v, "Tvector": B*v, - "Tcols": [{"i": i+1, "col": B.column(i)} for i in range(Tcolumns)], + "Tcolumns": [{"i": i+1, "col": B.column(i)} for i in range(Tcolumns)], } From a67c37dddcccf94b0e1af1d5a5f0ddb333fe8114 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Sun, 20 Apr 2025 16:58:55 -0500 Subject: [PATCH 7/9] Update template.xml --- .../linear-algebra/exercises/outcomes/AT/AT2/template.xml | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml b/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml index db70a4630..976225143 100644 --- a/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml +++ b/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml @@ -17,9 +17,9 @@ basis for \mathbb R^{{Scols}}.

- + S(\vec e_{ {{i}} }) = {{col}} - +

@@ -52,9 +52,9 @@ standard basis of \mathbb R^{{Tcols}}.

- + T(\vec e_{ {{i}} }) = {{col}} - +

From f43345e6eabd661d38902c79e7b36d704c4c57b5 Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Sun, 20 Apr 2025 16:59:25 -0500 Subject: [PATCH 8/9] Update generator.sage --- .../linear-algebra/exercises/outcomes/AT/AT2/generator.sage | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage b/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage index 4770e9419..547d87fa5 100644 --- a/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage +++ b/source/linear-algebra/exercises/outcomes/AT/AT2/generator.sage @@ -35,12 +35,12 @@ class Generator(BaseGenerator): "varmap": A*xs, "varvector": xs, "Sstandardmatrix": A, - "Scolumns": [{"i": i+1, "col": A.column(i)} for i in range(Scolumns)], + "Scolumns": [{"i": i+1, "col": column_matrix(A.column(i))} for i in range(Scolumns)], "Trows": Trows, "Tcols": Tcolumns, "Tstandardmatrix": B, "vector": v, "Tvector": B*v, - "Tcolumns": [{"i": i+1, "col": B.column(i)} for i in range(Tcolumns)], + "Tcolumns": [{"i": i+1, "col": column_matrix(B.column(i))} for i in range(Tcolumns)], } From 844dc0d8ccc76a6dbd6976afd92b25a39fa8347d Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Sun, 20 Apr 2025 17:00:23 -0500 Subject: [PATCH 9/9] Update template.xml --- .../linear-algebra/exercises/outcomes/AT/AT2/template.xml | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml b/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml index 976225143..e2ace68af 100644 --- a/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml +++ b/source/linear-algebra/exercises/outcomes/AT/AT2/template.xml @@ -16,9 +16,9 @@ basis for \mathbb R^{{Scols}}.

-

+

\hspace{1em} -S(\vec e_{ {{i}} }) = {{col}} +S(\vec e_{ {{i}} }) = {{col}} \hspace{1em}

@@ -51,9 +51,9 @@ standard basis of \mathbb R^{{Tcols}}.

-

+

\hspace{1em} -T(\vec e_{ {{i}} }) = {{col}} +T(\vec e_{ {{i}} }) = {{col}} \hspace{1em}