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由 Tzwan 於 星期六 六月 08, 2013 9:42 pm
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[大學][數學][問題]線代幾條問題
由 Rudolf166 於 星期三 十月 19, 2011 3:47 pm
1. Construct a system with more unknowns than equations, but no solution. Change the
right-hand side to zero and find all solutions x n .
2. Reduce A and B to echelon form, to find their ranks. Which variables are free?
A =
┌1 2 0 1┐
│0 1 1 0│
└1 2 0 1┘
B =
┌1 2 3┐
│4 5 6│
└7 8 9┘
Find the special solutions to Ax = 0 and Bx = 0. Find all solutions.
6. Describe the set of attainable right-hand sides b (in the column space) for
┌1 0┐ ┌b1 ┐
│0 1│┌u┐ = │b2 │
└2 3┘└v┘ └b3 ┘
by finding the constraints on b that turn the third equation into 0 = 0 (after elimination).
What is the rank, and a particular solution?
right-hand side to zero and find all solutions x n .
2. Reduce A and B to echelon form, to find their ranks. Which variables are free?
A =
┌1 2 0 1┐
│0 1 1 0│
└1 2 0 1┘
B =
┌1 2 3┐
│4 5 6│
└7 8 9┘
Find the special solutions to Ax = 0 and Bx = 0. Find all solutions.
6. Describe the set of attainable right-hand sides b (in the column space) for
┌1 0┐ ┌b1 ┐
│0 1│┌u┐ = │b2 │
└2 3┘└v┘ └b3 ┘
by finding the constraints on b that turn the third equation into 0 = 0 (after elimination).
What is the rank, and a particular solution?