Math 306 Homework
from Linear Algebra,
by Petersen
Chapter 1
1.4: 18
 Due 9/27  Problems 1,5 are to be carefully written up and separated from the rest of the HW.
 for 6, the line over γ means complex conjugate: If γ=a+bi, then conj(γ)=abi. The key properties of the conjugate that need verification are that
conj(γ_{1}γ_{2})=conj(γ_{1})conj(γ_{2}) and conj(γ_{1}+γ_{2})=conj(γ_{1})+conj(γ_{2}). Also if γ is real, note that conj(γ) = γ since the imaginary part of γ is 0.
 Solutions
1.5: 13,57,911
 Due 10/4
 for 2, p_{0}≠ 0.
 for 8, identify x_{i} with x_{i}+ i0 = (x_{i},0). Remember the complexification uses complex scalars.
 for 10, replace start of hint with: "Assume A ε M is such that some entry is nonzero. Make it 1, by multiplying A on the left by an appropriate matrix. Then show ..." Consider the effect of left and right multiplication of a matrix A by a standard basis vector E_{ij} described in example 10.
 Solutions
1.6: 2,4,5,6,810
1.7: 13,7,9
1.8: 13,5,11,13
1.9: 14
1.10: 16
1.11: 1,4,6,8
1.12: 2,4,8,9,10
Chapter 2
2.3: 1ab,2ab,3a,4ab,13,16,21
2.4: 1,4,6,7,8
2.5: 1ab,2ab,3a,4ab,8,13,15,18,19
 Due 12/8
 Most of the work for 14 was already done in section 3 HW
 Solutions
