From e335f9546c07ffe95f6f681e88961261a7ebb2d7 Mon Sep 17 00:00:00 2001 From: Tanaquil18 Date: Sun, 26 Jun 2022 01:53:39 +0000 Subject: [PATCH] Add titles to reading questions for Chapter VS (PR #102) --- src2/section-B.xml | 3 +++ src2/section-D.xml | 3 +++ src2/section-LISS.xml | 3 +++ src2/section-PD.xml | 3 +++ src2/section-S.xml | 3 +++ src2/section-VS.xml | 3 +++ 6 files changed, 18 insertions(+) diff --git a/src2/section-B.xml b/src2/section-B.xml index 985f614..8b3b0ab 100644 --- a/src2/section-B.xml +++ b/src2/section-B.xml @@ -706,6 +706,7 @@ + Columns of a nonsingular matrix

The matrix below is nonsingular. What can you now say about its columns?A=\begin{bmatrix} -3 & 0 & 1\\ @@ -715,11 +716,13 @@ + Linear combination of columns

Write the vector \vect{w}=\colvector{6\\6\\15} as a linear combination of the columns of the matrix A above. How many ways are there to answer this question?

 + Why desire orthonormal?

Why is an orthonormal basis desirable?

 diff --git a/src2/section-D.xml b/src2/section-D.xml index 42a8465..fce9f9c 100644 --- a/src2/section-D.xml +++ b/src2/section-D.xml @@ -568,16 +568,19 @@ + Calculate dimension of <m>P_6</m>

What is the dimension of the vector space P_6, the set of all polynomials of degree 6 or less?

 + Relate rank and nullity

How are the rank and nullity of a matrix related?

 + Rank of a nonsingular matrix

Explain why we might say that a nonsingular matrix has full rank.

 diff --git a/src2/section-LISS.xml b/src2/section-LISS.xml index 023ecb5..15cdf18 100644 --- a/src2/section-LISS.xml +++ b/src2/section-LISS.xml @@ -435,6 +435,7 @@ + Linear dependence of set of matrices

Is the set of matrices below linearly independent or linearly dependent in the vector space M_{22}? Why or why not?\set{ \begin{bmatrix} @@ -450,6 +451,7 @@ + Span vs. spans

Explain the difference between the following two uses of the term span:

  1. S is a subset of the vector space V and the span of S is a subspace of V.
    2. @@ -458,6 +460,7 @@ + Linear combination of vectors in linearly independent set

    The setS=\set{ \colvector{6\\2\\1},\, diff --git a/src2/section-PD.xml b/src2/section-PD.xml index bb633da..2fa4f8c 100644 --- a/src2/section-PD.xml +++ b/src2/section-PD.xml @@ -378,16 +378,19 @@ + Title of Theorem G

    Why does have the title it does?

         + Theorem RMRT surprising

    Why is so surprising ?

         + Calculate dimensions of the 4 subspaces

    Row-reduce the matrix A to reduced row-echelon form. Without any further computations, compute the dimensions of the four subspaces, (a) \nsp{A}, (b) \csp{A}, (c) \rsp{A} and (d) \lns{A}.A= \begin{bmatrix} diff --git a/src2/section-S.xml b/src2/section-S.xml index 3ae81e7..bd470db 100644 --- a/src2/section-S.xml +++ b/src2/section-S.xml @@ -707,16 +707,19 @@ + Subspace test

    Summarize the three conditions that allow us to quickly test if a set is a subspace.

         + Apply the subspace test

    Consider the set of vectorsW=\setparts{\colvector{a\\b\\c}}{3a-2b+c=5}. Is the set W a subspace of \complex{3}? Explain your answer.

         + Name five subspaces

    Name five general constructions of sets of column vectors (subsets of \complex{m}) that we now know as subspaces.

     diff --git a/src2/section-VS.xml b/src2/section-VS.xml index 107145c..8b77e23 100644 --- a/src2/section-VS.xml +++ b/src2/section-VS.xml @@ -553,16 +553,19 @@ + Complex vector space

    Comment on how the vector space \complex{m} went from a theorem () to an example ().

         + Calculate linear combination in Crazy Vector Space

    In the crazy vector space, C, () compute the linear combination2(3,\,4)+(-6)(1,\,2).

         + Why prove things about the zero vector?

    Suppose that \alpha is a scalar and \zerovector is the zero vector. Why should we prove anything as obvious as \alpha\zerovector=\zerovector such as we did in ?