From 36a03a020b6e92e8a636e7976c39eeb54f1b873c Mon Sep 17 00:00:00 2001 From: Tanaquil18 Date: Fri, 24 Jun 2022 01:18:57 +0000 Subject: [PATCH] Add titles to reading questions in Chapter SLE (PR #101) --- src2/section-HSE.xml | 3 +++ src2/section-NM.xml | 3 +++ src2/section-RREF.xml | 3 +++ src2/section-SSLE.xml | 3 +++ src2/section-TSS.xml | 3 +++ src2/section-WILA.xml | 3 +++ 6 files changed, 18 insertions(+) diff --git a/src2/section-HSE.xml b/src2/section-HSE.xml index 5e2247c..33c6b90 100644 --- a/src2/section-HSE.xml +++ b/src2/section-HSE.xml @@ -320,16 +320,19 @@ + Solution set of a homogeneous system

What is always true of the solution set for a homogeneous system of equations?

 + Solution set with more variables than equations

Suppose a homogeneous system of equations has 13 variables and 8 equations. How many solutions will it have? Why?

 + Null space in words

Describe, using only words, the null space of a matrix. (So in particular, do not use any symbols.)

 diff --git a/src2/section-NM.xml b/src2/section-NM.xml index 74a2407..7714ddb 100644 --- a/src2/section-NM.xml +++ b/src2/section-NM.xml @@ -351,16 +351,19 @@ + Definition of nonsingular

In your own words state the definition of a nonsingular matrix.

 + How to recognize nonsingular?

What is the easiest way to recognize if a square matrix is nonsingular or not?

 + Solution set of system with nonsingular coefficient matrix

Suppose we have a system of equations and its coefficient matrix is nonsingular. What can you say about the solution set for this system?

 diff --git a/src2/section-RREF.xml b/src2/section-RREF.xml index 4e03fb6..baa90e6 100644 --- a/src2/section-RREF.xml +++ b/src2/section-RREF.xml @@ -1159,6 +1159,7 @@ + Matrix in RREF?

Is the matrix below in reduced row-echelon form? Why or why not?\begin{bmatrix} 1 & 5 & 0 & 6 & 8\\ @@ -1168,6 +1169,7 @@ + Calculate RREF of a matrix

Use row operations to convert the matrix below to reduced row-echelon form and report the final matrix.\begin{bmatrix} 2 & 1 & 8\\ @@ -1177,6 +1179,7 @@ + Calculate system's solution set, report RREF

Find all the solutions to the system below by using an augmented matrix and row operations. Report your final matrix in reduced row-echelon form and the set of solutions. 2x_1 + 3x_2 - x_3&= 0 diff --git a/src2/section-SSLE.xml b/src2/section-SSLE.xml index f1ee637..7410030 100644 --- a/src2/section-SSLE.xml +++ b/src2/section-SSLE.xml @@ -455,16 +455,19 @@ + Number of solutions of a linear system

How many solutions does the system of equations 3x + 2y = 4, 6x + 4y = 8 have? Explain your answer.

 + Number of solutions of a different linear system

How many solutions does the system of equations 3x + 2y = 4, 6x + 4y = -2 have? Explain your answer.

 + How mathematics is a language

What do we mean when we say mathematics is a language?

 diff --git a/src2/section-TSS.xml b/src2/section-TSS.xml index e9d9c39..6bc9ef6 100644 --- a/src2/section-TSS.xml +++ b/src2/section-TSS.xml @@ -442,16 +442,19 @@ + How to analyze consistency?

How can we easily recognize when a system of linear equations is inconsistent or not?

 + How to identify independent/dependent variables?

Suppose we have converted the augmented matrix of a system of equations into reduced row-echelon form. How do we then identify the dependent and independent (free) variables?

 + Possibilities for solution sets

What are the possible solution sets for a system of linear equations?

 diff --git a/src2/section-WILA.xml b/src2/section-WILA.xml index ee7c424..b627492 100644 --- a/src2/section-WILA.xml +++ b/src2/section-WILA.xml @@ -207,16 +207,19 @@ + Whether a given equation is linear

Is the equation x^2 + xy +\tan(y^3)=0 linear or not? Why or why not?

 + Solve a linear system, 2 equations, 2 unknowns

Find all solutions to the system of two linear equations 2x+3y=-8, x-y=6.

 + Usefulness of linear systems

Describe how the production manager might explain the importance of the procedures described in the trail mix application ().