601-hw-v

# 601-hw-v - MATH 601, AUTUMN 2008 Additional homework V,...

This preview shows pages 1–2. Sign up to view the full content.

Additional homework V, October 30 PROBLEMS 1. Find the solution v ( t ) = ( x ( t ) , y ( t ) , z ( t )) to the system of ordinary diﬀerential equations ˙ v = Tv with the initial condition v (0) = (1 , 1 , 1), where T : R 3 R 3 is the operator T x y z = 1 - 2 2 1 - 1 3 0 0 2 · x y z , with vectors of R 3 written in the column form. 2. Find an explicit formula for the solutions x ( t ) , y ( t )) to the system of ordinary diﬀerential equations ˙ x = 3 x - 9 y , ˙ y = x - 3 y with any given initial conditions x (0) = a , y (0) = b , a, b C . 3. Let T End R 4 be the linear operator given by T x y z u = - 1 1 1 - 2 0 0 - 1 0 0 0 1 0 0 0 0 1 · x y z u , with vectors of R 4 written in the column form. Find all eigenvalues of T and construct a basis for each eigenspace of T . 4. Evaluate T 38 w for w = (1 , 1 , 1) R 3 and the operator T : R 3 R 3 deﬁned by T x y z = 15 40 - 17 10 25 - 11 36 92 - 40 · x y z . (No calculators, please!)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/18/2009 for the course MATH 601 taught by Professor Un during the Fall '08 term at Ohio State.

### Page1 / 4

601-hw-v - MATH 601, AUTUMN 2008 Additional homework V,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online