A x = 1 -4 9-36 -12 let ai be the first column vector of A, and a2 be the second column vector of A. Let nontrivial solution of x₁ẫ₁ + x2ả₂ = Ō by inspection. = [2]. X2 Find one
A x = 1 -4 9-36 -12 let ai be the first column vector of A, and a2 be the second column vector of A. Let nontrivial solution of x₁ẫ₁ + x2ả₂ = Ō by inspection. = [2]. X2 Find one
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![In this exercise, you are given the matrix \( A \) defined as:
\[
A = \begin{bmatrix} 1 & -4 \\ 9 & -36 \\ 3 & -12 \end{bmatrix}
\]
Let \(\vec{a}_1\) be the first column vector of \( A \), and \(\vec{a}_2\) be the second column vector of \( A \). We define the vector \(\vec{x}\) as:
\[
\vec{x} = \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}
\]
The task is to find one nontrivial solution for the equation \( x_1 \vec{a}_1 + x_2 \vec{a}_2 = \vec{0} \) by inspection, where \( \vec{0} \) is the zero vector.
There is also a blank vector representation shown, indicating that the solution could be filled in as:
\[
\vec{x} = \begin{bmatrix} \, \\ \, \end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18574973-f25e-4ab8-b7d6-6007b5b87fc4%2F49114ca0-97d7-498b-b38c-c5873a882735%2F56km7m3_processed.png&w=3840&q=75)
Transcribed Image Text:In this exercise, you are given the matrix \( A \) defined as:
\[
A = \begin{bmatrix} 1 & -4 \\ 9 & -36 \\ 3 & -12 \end{bmatrix}
\]
Let \(\vec{a}_1\) be the first column vector of \( A \), and \(\vec{a}_2\) be the second column vector of \( A \). We define the vector \(\vec{x}\) as:
\[
\vec{x} = \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}
\]
The task is to find one nontrivial solution for the equation \( x_1 \vec{a}_1 + x_2 \vec{a}_2 = \vec{0} \) by inspection, where \( \vec{0} \) is the zero vector.
There is also a blank vector representation shown, indicating that the solution could be filled in as:
\[
\vec{x} = \begin{bmatrix} \, \\ \, \end{bmatrix}
\]
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