BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 22 U. Muan g July 4, 2008
Homework problems from the 2nd Edition, SECTION 6.3
15(15)2 The C.E. p() = 2 - 3 + 2 = ( - 2)( - 1)2 =
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 21 U. Muan g July 4, 2008
Homework problems from the 2nd Edition, SECTION 6.2
15(15)2 The characteristic eq. p() = -3 + 22 - = -
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 20 U. Muan g July 4, 2008
Homework problems from the 2nd Edition, SECTION 6.1
3(3)2 The characteristic eq. p() = 2 - 7 + 10 = 0.
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 19 U. Muan g 1) a) Corresponding homogenous equation is y - y - 2y = 0 Since, it is a constant coefficient D.E. we look for the
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Homework set # 19 U.Muan g July 16, 2008
VARIATION OF PARAMETERS 1) Find a particular solution of the following D.E. by using the variation of parameters. T
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 18 U. Muan g 1) a) First we find the solution of the corresponding homogenous D.E. y - 2y - 3y = 0, which has the C.E. r2 - 2r -
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Homework set # 18 U.Muan g July 16, 2008
METHOD OF UNDETERMINED COEFFICIENTS 1) Find the general solution of the following D.E's a) y - 2y - 3y = 3e2x . b)
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 17 U. Muan g July 16, 2008
1) a) Substituting y = erx into the D.E., we get the C.E. r2 - 2r + 1 = 0 which gives r1 = r2 = 1. Th
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Homework set # 17 U.Muan g July 16, 2008
REPEATED ROOTS; REDUCTION OF ORDER 1) a) b) c) 2) a) b) c) 3) a) b) c) 4) Find the general solution of the followin
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 16 U. Muan g July 16, 2008
1) a) W (e2x , e-3x/2 ) = b) W (x, xex ) = c) W (ex sin x, ex cos x) = ex sin x ex cos x = -e2x ex si
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS Homework set # 16 U.Muan g July 16, 2008
FUNDAMENTAL SET OF SOLUTIONS 1) a) b) c) Find the Wronskian of the following given pair of functions: e2x , e-3x/2 .
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 15 U. Muan g July 2, 2008
Homework problems from the 2nd Edition, SECTION 4.5
5) 1 0 -2 0 E = 0 1 3 0 . 0 0 0 1
Row basis: The
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 15-A U. Muan g July 2, 2008
Homework problems from the 2nd Edition, SECTION 4.6
4) Yes, the three vectors are mutually orthogona
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 14 U. Muan g July 2, 2008
Homework problems from the 2nd Edition, SECTION 4.4
3(3)2 Any four vectors in R3 are L.D., so the give
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 13 U. Muan g July 2, 2008
Homework problems from the 2nd Edition, SECTION 4.3
3(3)2 Clearly any three vectors in R2 are L.D. Sin
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 12 U. Muan g July 2, 2008
Homework problems from the 2nd Edition, SECTION 4.2
3(3)2 A typical vector in W is of the form x = (x1
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 11 U. Muan g July 2, 2008
Homework problems from the 2nd Edition, SECTION 4.1
3(3)2 |a - b| = |(2i - 3j + 5k) - (5i + 3j - 7k)|
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 10 U. Muan g July 2, 2008
Homework problems from the 2nd Edition, SECTION 3.6
23(23)2 The coefficient matrix A is A= and det A =
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 9 U. Muan g July 2, 2008
Homework problems from the 2nd Edition, SECTION 3.5
3(3)2 A-1 = 5(5) A-1 = 7(7) A-1 = 11(11) Let 1 7 -9
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 8 U. Muan g July 2, 2008
Homework problems from the 2nd Edition, SECTION 3.4
5(5)2 2 -1 3 2 8(8) 3 0 1 0 3 21 15 -1 4 = , 2 -5 4
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 7 U. Muan g June 20, 2008
Homework problems from the 2nd Edition, SECTION 3.3
3(3)2 Let A= 3 7 15 2 5 11
Do the following row op
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 6 U. Muan g June 20, 2008
Homework problems from the 2nd Edition, SECTION 3.2
3(3)2 Since the linear system is already in echelo
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 5 U. Muan g June 20, 2008
Homework problems from the 2nd Edition, SECTION 3.1
3(3)2 Substruction of 3/2 times the first equation
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 4 U. Muan g June 20, 2008
Homework problems from the 2nd Edition, SECTION 1.6
3
(3) 2
Let v = y/x then D.E. leads to following s
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 3 U. Muan g June 20, 2008
Homework problems from the 2nd Edition, SECTION 1.5
5
(5) 2
Linear first order D.E. which can be solve
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 2 U. Muan g June 13, 2008
Homework problems from the 2nd Edition, SECTION 1.4
3 (3)2 The given D.E. is separable, so if we separ
BILKENT UNIVERSITY Department of Mathematics MATH 225, LINEAR ALGEBRA and DIFFERENTIAL EQUATIONS, Solution of Homework set1 # 1 U. Muan g June 13, 2008
Homework problems from the 2nd Edition, SECTION 1.3
12
(22) 2
Since, f (x, y) = x ln y, and
f x = y y