diff --git a/source/linear-algebra/exercises/outcomes/MX/MX2/generator.sage b/source/linear-algebra/exercises/outcomes/MX/MX2/generator.sage index c746b4e2d..99bdc9b2e 100644 --- a/source/linear-algebra/exercises/outcomes/MX/MX2/generator.sage +++ b/source/linear-algebra/exercises/outcomes/MX/MX2/generator.sage @@ -14,7 +14,7 @@ class Generator(BaseGenerator): constants = A*solution m = A.augment(constants, subdivide=True) ordinal = randrange(1,4) - ordinal_string = ["1st", "2nd", "3rd", "4th"][ordinal] + ordinal_string = ["first", "second", "third", "fourth"][ordinal] ord_matrix = A.augment(column_matrix( identity_matrix(4).column(ordinal)), subdivide=True) @@ -43,6 +43,7 @@ class Generator(BaseGenerator): "invertible": False, "label": labels[1], "vector_eq": TBIL.VectorEquation(m), + "ordinal": ordinal_string, }] shuffle(matrices) diff --git a/source/linear-algebra/exercises/outcomes/MX/MX2/template.xml b/source/linear-algebra/exercises/outcomes/MX/MX2/template.xml index e91a16524..30be28e26 100644 --- a/source/linear-algebra/exercises/outcomes/MX/MX2/template.xml +++ b/source/linear-algebra/exercises/outcomes/MX/MX2/template.xml @@ -25,10 +25,10 @@ discussing its corresponding linear transformation.

-{{label}} is invertible. +{{label}} is invertible because its transformation is bijective. -{{label}} is not invertible. +{{label}} is not invertible because its transformation is not bijective.

@@ -36,13 +36,19 @@ discussing its corresponding linear transformation.

-If the matrix is invertible, use technology to find its inverse. +If the matrix is invertible, explain and demonstrate how to find the +{{ordinal}} column of this inverse by solving an appropriate linear system +or vector equation.

-Its inverse is {{inverse}}. +Since + +\operatorname{RREF} {{ord_matrix}} = {{ord_rref}} + +the {{ordinal}} column of the inverse is {{ord_col}}. N/A @@ -53,20 +59,13 @@ N/A

-If the matrix is invertible, explain and demonstrate how to find the -{{ordinal}} column of this inverse using a technique that could be -performed without technology (though you may use technology for this -exercise). +If the matrix is invertible, use technology to find its inverse.

-Since - -\operatorname{RREF} {{ord_matrix}} = {{ord_rref}} - -the {{ordinal}} column of the inverse is {{ord_col}}. +Its inverse is {{inverse}}. N/A