MA232_Test2_Practice

# MA232_Test2_Practice - of a matrix A type inv(A 2.2...

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MA232 Fall 2008 Test 2 Practice October 3, 2008 The answers to the practice problems below will be posted on the website soon. 1 Variation of Parameters (Euler-Lagrange Method) Solve the following problems from pg.71 using Variation of Parameters . Use the initial con- ditions given here.: problem 22, y (0)=1 problem 23, y (0)=-1 problem 24, y (0)=1 problem 26, y (0)=0 problem 27, y (0)=1 problem 28, y (0)=1 problem 29, y (1)=1 Also look at problem 1 from the summer test. There will be 3 problems like this, each worth 20 points. 2 Linear Algebra 2.1 Marix Operations These problems will add up to 15 points. 1

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2.1.1 Multiplication/Addition/Subtraction Summer test problems 2a-2d pg. 127: 5,11 Make up your own problem and check with Matlab. For example, to type the matrix A on page 127 into Matlab, type A=[-1 0 2;2 1 2;-1 0 1] and then to multiply A by itself type A*A 2.1.2 Matrix Inverse Summer Test problem 2e. Make up 2x2 matrices and check with Matlab. To ﬁnd the inverse
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Unformatted text preview: of a matrix, A, type inv(A) 2.2 Eigenstuﬀ and Determinants These problems will add up to 25 points 2.2.1 Determinants Summer Test problems 3a and 3b. Make up 2x2 and 3x3 matrices and check with Matlab. To ﬁnd the determinant of a matrix, A, type det(A). 2.2.2 2x2 Eigenvalues and Eigenvectors For the following problems, ﬁnd the eigenvalues and eigenvectors: • summer test problem 3c (last page) • pg.324: 3-6, 8, 11 • make up you own and test with Matlab using [V,D]=eig(A,’nobalance’). The eigen-vectors are the columns of V and the eigenvalues are along the diagonal of D. **remember that your eigenvectors may be oﬀ by a factor on both numbers; this is OK. 2.2.3 3x3 Eigenvalues Find the eigenvalues for the following problems: • summer test problem 3d (2nd to last page) • pg.324: 19, 22, 24, 27-30 (just eigenvalues) 2...
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## This note was uploaded on 08/31/2009 for the course MA 232 taught by Professor Toland during the Spring '08 term at Clarkson University .

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MA232_Test2_Practice - of a matrix A type inv(A 2.2...

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