Solved: In Exercises 5 and 6, follow the method of

Chapter 1, Problem 6E

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Problem 6E

In Exercises 5 and 6, follow the method of Examples 1 and 2 to write the solution set of the given homogeneous system in parametric vector form.

${x}_{1}\ +\ 2{x}_{2}\ -\ 3{x}_{3}\ =\ 0$

$2{x}_{1}\ +\ {x}_{2}\ -\ 3{x}_{3}\ =\ 0$

$-1{x}_{1}\ +\ {x}_{2}\ \ \ \ \ \ \ \ \ \ =\ 0$

Example 1: Determine if the following homogeneous system has a nontrivial solution. Then describe the solution set.

$3{x}_{1}\ +\ 5{x}_{2}\ -\ 4{x}_{3}\ =\ 0$

$-3{x}_{1}\ -\ 2{x}_{2}\ +\ 4{x}_{3}\ =\ 0$

$6{x}_{1}\ +\ {x}_{2}\ -8{x}_{3}\ =\ 0$

Example 2: A single linear equation can be treated as a very simple system of equations. Describe all solutions of the homogeneous “system”

$10{x}_{1}\ -\ 3{x}_{2}\ -\ 2{x}_{3}\ =\ 0$

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