Linear Algebra and Its Applications, 5th Edition
Authors: David C. Lay, Steven R. Lay, Judi J. McDonald
ISBN-13: 978-0321982384
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See our solution for Question 33E from Chapter 1.5 from Lay's Linear Algebra and Its Applications, 5th Edition.
Problem 33E
Chapter:
Problem:
Given A = find one nontrivial solution of Ax = 0 by inspection. [Hint: Think of the equation Ax = 0 written as a vector equation.]
Step-by-Step Solution
Given Information
We are given with following matrix: \[ A = \left[ \begin{array} { r r } { - 2 } & { - 6 } \\ { 7 } & { 21 } \\ { - 3 } & { - 9 } \end{array} \right] \] We have to find one nontrivial solution of $Ax=0$ by inspection.
Step-1:
Let, \[ x = \left[ \begin{array} { l } { x _ { 1 } } \\ { x _ { 2 } } \end{array} \right] \] Write the matrix equation: \[ x _ { 1 } \left[ \begin{array} { c } { - 2 } \\ { 7 } \\ { - 3 } \end{array} \right] + x _ { 2 } \left[ \begin{array} { c } { - 6 } \\ { 21 } \\ { - 9 } \end{array} \right] = 0 \] By inspection, the solution of the equation is: \[{x_1} = - 3;\,\,{x_2} = 1\]
\[{\bf{x}} = \left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 3}\\ 1 \end{array}} \right]\]
We are given with following matrix: \[ A = \left[ \begin{array} { r r } { - 2 } & { - 6 } \\ { 7 } & { 21 } \\ { - 3 } & { - 9 } \end{array} \right] \] We have to find one nontrivial solution of $Ax=0$ by inspection.
Step-1:
Let, \[ x = \left[ \begin{array} { l } { x _ { 1 } } \\ { x _ { 2 } } \end{array} \right] \] Write the matrix equation: \[ x _ { 1 } \left[ \begin{array} { c } { - 2 } \\ { 7 } \\ { - 3 } \end{array} \right] + x _ { 2 } \left[ \begin{array} { c } { - 6 } \\ { 21 } \\ { - 9 } \end{array} \right] = 0 \] By inspection, the solution of the equation is: \[{x_1} = - 3;\,\,{x_2} = 1\]
\[{\bf{x}} = \left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{x_2}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 3}\\ 1 \end{array}} \right]\]