1) 2) 3) 4) & 5) for 3b ( the one above) Compute the eigenvalues of each of the

Question

1)

2)

3)

4) & 5) for 3b ( the one above)

Compute the eigenvalues of each of the following matrices. Determine an eigenvector with the largest eigenvalue. In each of the following sets of three equations, show that the third equation equals the second equation minus multiple of the first equation: (c) = (b) - r(a) for some r. Solve the following systems of equations using Gaussian elimination. Write the LU decomposition for each coefficient matrix A in Exercise 3. Multiply L times U to show that the product is A, for each coefficient matrix A in Exercise 3. Find the determinant of each matrix in Exercise 3 using Theorem 2. Solve the following systems of equations using Gaussian elimination.

Explanation / Answer

1i)?1=4, ?2=2

1ii)

1iii)?1=4, ?2=1

1iv)?1=3, ?2=3

1v) ?1=2, ?2=-1, ?3=1

first number 3)

last 3b) x1=1/3, x2=-7/3, x3=0

x1 = 1/3 x2 = -7/3 x3 = 0

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