Question 7 Consider the matrix 5 1 1 4 2 1 2 1 A= 4 (a) or Positive definite? (Justify your answers.) Show that the matrix A is invertible. Is the matrix A symmetric? Strictly diagonally dominant?

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.2: Diagonalization
Problem 45E
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Part A

Question 7
Consider the matrix
1
1
1 4 2
1 2 4
A =
(a)
or Positive definite? (Justify your answers.)
Show that the matrix A is invertible. Is the matrix A symmetric? Strictly diagonally dominant?
(b)
positive diagonal entries such that A = LDLT.
Determine a lower triangular matrix L with 1s on its diagonal and D a diagonal matrix with
Transcribed Image Text:Question 7 Consider the matrix 1 1 1 4 2 1 2 4 A = (a) or Positive definite? (Justify your answers.) Show that the matrix A is invertible. Is the matrix A symmetric? Strictly diagonally dominant? (b) positive diagonal entries such that A = LDLT. Determine a lower triangular matrix L with 1s on its diagonal and D a diagonal matrix with
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