Subject name: Linear AlgebraTips: solve problem-1 must do it handwriting on a paper Assignment -12Problem 1: Diagonalize A and compute SAKS-¹ to prove this formulafor AK: MAAA =Problem 2: Let5 10 4Bin Han (HDU)A =has Ak-[0--2 010 2-12Diagonalizing a Matrix05k - 4k4*].4k(1) Find the eigenvalues and eigenvectors of A;(2) Find an invertible matrix S such that SAS to be a diagonal matrix;(3) Compute A", where m is a positive integer.13/14

Answered: Problem 1: Diagonalize A and compute…

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Problem 1: Diagonalize A and compute SAS-¹ to prove this formula for Ak: A 1 - [54] has Ak A² = [* 04 5k 5k - 4k 0 ].

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.4: The Singular Value Decomposition

Problem 26EQ

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Question

Subject name: Linear Algebra

Tips: solve problem-1 must do it handwriting on a paper

Assignment -12
Problem 1: Diagonalize A and compute SAKS-¹ to prove this formula
for AK: MAA
A =
Problem 2: Let
5 1
0 4
Bin Han (HDU)
A =
has Ak
-[
0
-
-2 0
1
0 2
-1
2
Diagonalizing a Matrix
0
5k - 4k
4*].
4k
(1) Find the eigenvalues and eigenvectors of A;
(2) Find an invertible matrix S such that SAS to be a diagonal matrix;
(3) Compute A", where m is a positive integer.
13/14

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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