Linear algebra: please solve q13, 14 correctly and handwritten, equ 4 also attached Using Eq. (4), apply the singularity test to the matrices inExercises 13-16. Show that there is no real scalar > suchthat A-I is singular. [Note: Complex eigenvalues arediscussed in Section 4.6.]-2-2 -15213. A =15. A =2]2- -11214. A =16. A =3-25-3111 If we apply the result in (3b) to the matrix A-XI, it follows that A - 27 is singular ifand only if λ is a value such that(a)(d) - bc = 0.(4)Expanding the equation for λ given above, we obtain the following condition on λ:λ² (a + d) + (ad - bc) = 0.

Answered: Image /qna-images/answer/6bbdcbc0-69bd-408f-8dae-22cc36a6753f.jpg

Answered: Using Eq. (4), apply the singularity…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 10AEXP

See similar textbooks

Related questions

Question

Linear algebra: please solve q13, 14 correctly and handwritten, equ 4 also attached

Using Eq. (4), apply the singularity test to the matrices in
Exercises 13-16. Show that there is no real scalar > such
that A-I is singular. [Note: Complex eigenvalues are
discussed in Section 4.6.]
-2
-2 -1
52
13. A =
15. A =
2]
2- -1
1
2
14. A =
16. A =
3-2
5-3
1
1
1

If we apply the result in (3b) to the matrix A-XI, it follows that A - 27 is singular if
and only if λ is a value such that
(a)(d) - bc = 0.
(4)
Expanding the equation for λ given above, we obtain the following condition on λ:
λ² (a + d) + (ad - bc) = 0.

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.

Expert Solution