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Let A be a matrix given by 3-6 -1 4 -8 -2 -3 6 3 Find a 3x3 matrix B such that B 0 and AB = 0. A =

Let A be a matrix given by 3-6 -1 4 -8 -2 -3 6 3 Find a 3x3 matrix B such that B 0 and AB = 0. A =

Advanced Engineering Mathematics
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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**Matrix Input Section** **Instruction:** - **Enter the matrix \( B \):** - A blank input field is provided for entering the matrix \( B \). Ensure the matrix is entered in the proper format, using commas and spaces as necessary to separate elements and rows. **Visual Aid:** - Below the input field, there is a checkbox that may be used for additional options or to confirm the input of the matrix. This enhances the input process ensuring accuracy and completion.
Transcribed Image Text:**Matrix Input Section** **Instruction:** - **Enter the matrix \( B \):** - A blank input field is provided for entering the matrix \( B \). Ensure the matrix is entered in the proper format, using commas and spaces as necessary to separate elements and rows. **Visual Aid:** - Below the input field, there is a checkbox that may be used for additional options or to confirm the input of the matrix. This enhances the input process ensuring accuracy and completion.
Let \( A \) be a matrix given by \[ A = \begin{bmatrix} 3 & -6 & -1 \\ 4 & -8 & -2 \\ -3 & 6 & 3 \end{bmatrix} \] Find a \( 3 \times 3 \) matrix \( B \) such that \( B \neq 0 \) and \( AB = 0 \).
Transcribed Image Text:Let \( A \) be a matrix given by \[ A = \begin{bmatrix} 3 & -6 & -1 \\ 4 & -8 & -2 \\ -3 & 6 & 3 \end{bmatrix} \] Find a \( 3 \times 3 \) matrix \( B \) such that \( B \neq 0 \) and \( AB = 0 \).
Expert Solution
Step 1: Finding the matrix B

A=3-6-14-8-2-363

Finding the eigen value of the matrix A

A-λI=3-λ-6-14-8-λ-2-36-λ3-λ            =λλ2+2λ-6

Hence λ=0 is one of the eigen value of A

So the determinant of 0

So for any non-singular matrix AB=0

Say B=100010001

AB=AI=A=0 

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