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DEPARTMENT OF MATHEMATICS
UNIVERSITY OF QUEENSLAND
PROBLEMS 1.6 ... 1
PROBLEMS 2.4 ... 12
PROBLEMS 2.7 ... 18
PROBLEMS 3.6 ... 32
PROBLEMS 4.1 ... 45
PROBLEMS 5.8 ... 58
PROBLEMS 6.3 ... 69
PROBLEMS 7.3 ... 83
PROBLEMS 8.8 ... 91
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matrix, skew–symmetric, 46 matrix, subtraction, 24 matrix, symmetric, 46 matrix, transpose, 45 matrix, unit vectors, 28 matrix, zero, 24. modular addition, 4 modular
We continue our study of matrices by considering an important class of subsets of F n called subspaces.. These arise naturally for example, when we solve a system of m linear
If A is upper triangular, equation 4.1 remains true and the proof is again an exercise in induction, with the slight difference that the column version of theorem 4.0.1 is
If the line is given as the intersection of two planes, each in normal form, there is a simple way of finding an equation for this plane.. Let A, B, C be
matrix, skew–symmetric, 46 matrix, subtraction, 24 matrix, symmetric, 46 matrix, transpose, 45 matrix, unit vectors, 28 matrix, zero, 24. modular addition, 4 modular multiplication,
This problem is a special case of a more general result about Markov
Then the homogeneous system BX = 0 has a non–trivial solution X 0, as the number of unknowns is greater than the number of equations. Consequently AB is
Then these points determine a circle.. Then there are
