Linear algebra : please provide me detail and accurate solution Let A be a 3 x 3 matrix:A =a11a12 a13a21 a22 a23a31 a32 a33The entries aj, i, j = 1, 2, 3 are numbers.Let A be an eigenvalue of A. For i, j = 1,2,3, denote by Mij the (i, j)-minor of A-XI,where I is the 3 x 3 identity matrix.Show that the following vector-det (M₂1)det (M22)-det (M23)is an eigenvector of A with eigenvalue X. Show your work in details.

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Answered: Let A be a 3 x 3 matrix: A = a11 a12…

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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Linear algebra : please provide me detail and accurate solution

Let A be a 3 x 3 matrix:
A =
a11
a12 a13
a21 a22 a23
a31 a32 a33
The entries aj, i, j = 1, 2, 3 are numbers.
Let A be an eigenvalue of A. For i, j = 1,2,3, denote by Mij the (i, j)-minor of A-XI,
where I is the 3 x 3 identity matrix.
Show that the following vector
-det (M₂1)
det (M22)
-det (M23)
is an eigenvector of A with eigenvalue X. Show your work in details.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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