1.Let A be a square matrix whose Jordan canonical form is(1 1 0 0 0 0 0 0 00 1 1 0 0 0 0 0 00 0 10 0 0 0 000 0 0 1 0 0 0 0 00 0 0 0 2 10 000 0 0 0 0 2 0 0 00 0 0 0 0 0 2 1 00 0 0 0 0 00 0 0 0 00 0 20 0 2 0(a) Is A nonsingular? Explain.(b) Write down all the eigenvalues of A and their algebraic and geometricmultiplicities.(c) Let K be the nullspace of (A – I)? where I is the 9 x 9 identity matrix.Evaluate dim K.

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1. Let A be a square matrix whose Jordan canonical form is '1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 00 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 10 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2, 0 0 0 0 0 (a) Is A nonsingular? Explain. (b) Write down all the eigenvalues of A and their algebraic and geometric multiplicities. (c) Let K be the nullspace of (A – I)? where I is the 9 x 9 identity matrix. Evaluate dim K.

1. Let A be a square matrix whose Jordan canonical form is '1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 00 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 10 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2, 0 0 0 0 0 (a) Is A nonsingular? Explain. (b) Write down all the eigenvalues of A and their algebraic and geometric multiplicities. (c) Let K be the nullspace of (A – I)? where I is the 9 x 9 identity matrix. Evaluate dim K.

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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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

1.
Let A be a square matrix whose Jordan canonical form is
(1 1 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0
0 0 10 0 0 0 00
0 0 0 1 0 0 0 0 0
0 0 0 0 2 10 00
0 0 0 0 0 2 0 0 0
0 0 0 0 0 0 2 1 0
0 0 0 0 0 0
0 0 0 0 00 0 2
0 0 2 0
(a) Is A nonsingular? Explain.
(b) Write down all the eigenvalues of A and their algebraic and geometric
multiplicities.
(c) Let K be the nullspace of (A – I)? where I is the 9 x 9 identity matrix.
Evaluate dim K.

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