Question

Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D such that A= PDP^-1. A = [[4, 0, 0, 0], [0, 4, 0, 0], [1, -4, -4, 0], [-1, 2, 0, -4]]

          Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D such that A= PDP^-1.

A = [[4, 0, 0, 0], [0, 4, 0, 0], [1, -4, -4, 0], [-1, 2, 0, -4]]

Added by Francisco H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

05/24/2022

Step 1

The characteristic equation is det(A - λI) = (4 - λ)^2(-4 - λ)^2 = 0. Solving for λ, we get λ = 4 (with multiplicity 2) and λ = -4 (with multiplicity 2). ** Show more…

Show all steps