Find a 3 x 3 matrix A that has eigenvalues400QO=0, 12, -12, with corresponding eigenvectorsrespectively. Enter the first column of A, in order, into the answer box below, separated with commas. i.e., enterthe values of a11, a21, and a31 (in that order).

We have to find a matrix that has eigenvalues , with the corresponding eigenvectorsWe know thatIf A…

Answered: Find a 3 x 3 matrix A that has…

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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Find a 3 x 3 matrix A that has eigenvalues
400
QO
=
0, 12, -12, with corresponding eigenvectors
respectively. Enter the first column of A, in order, into the answer box below, separated with commas. i.e., enter
the values of a11, a21, and a31 (in that order).

Expert Solution

Step 1: Introduction

We have to find a $3 cross times 3$ matrix that has eigenvalues $lambda equals 0 comma space 12 comma space minus 12$ , with the corresponding eigenvectors

$open square brackets table row 0 row 1 row cell negative 1 end cell end table close square brackets space comma space open square brackets table row 1 row 1 row 1 end table close square brackets space comma space open square brackets table row 0 row 1 row 1 end table close square brackets$

We know that

If A is n×n matrix and A has n distinct eigenvalues, then A is digonalizable matrix.