Take your timeSolve all three parts in the order to get positive feedback please show me neat and clean work for it by hand solution for kindly solve ? percent accuracy please do all parts via by hand solution Problem 3.Assume that A is a n x n real matrix. We define the exponential of A, as the series1e^= 1+A+A²where I is the n x n identity matrix.a) Show that forA+.where a and b are 2 real numbers, we haveeª(8=a= (8 %)1n!0 eb02).A" +...b) Show that if B € M₂ (R) is similar to a diagonal matrix D with a transition matrixdenoted by P (that is B = PDP ¹) theneB Pepp 1c) Show that if A and B are 2 matrices such that AB = BA, then eA¹B = eA eB

Let A be any n×n real matrix then, eA=I+A+A22!+A33!+... To Prove: (a) If A=a00b then eA=ea00eb.…

Problem 3. Assume that A is a nx n real matrix. We define the exponential of A, as the series 1 e^ = 1+A+ A²+₁ where I is the n x n identity matrix. a) Show that for a A-(88) А 0 b where a and b are 2 real numbers, we have 1 n! AT +... 0 *-(69). 0 eb b) Show that if B € M₂ (R) is similar to a diagonal matrix D with a transition matrix denoted by P (that is B = PDP ¹) then e³ = Pepp ¹. A c) Show that if A and B are 2 matrices such that AB = BA, then eA¹B — eªcB =

Problem 3. Assume that A is a nx n real matrix. We define the exponential of A, as the series 1 e^ = 1+A+ A²+₁ where I is the n x n identity matrix. a) Show that for a A-(88) А 0 b where a and b are 2 real numbers, we have 1 n! AT +... 0 *-(69). 0 eb b) Show that if B € M₂ (R) is similar to a diagonal matrix D with a transition matrix denoted by P (that is B = PDP ¹) then e³ = Pepp ¹. A c) Show that if A and B are 2 matrices such that AB = BA, then eA¹B — eªcB =

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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