6.1 and 6.2 Flashcards
What is an nxm matrix?
A rectangular array of numbers with n rows and m coloumns
List some examples of how to create matrices in Matlab.
- A = [1 2; 2 3]
- zeroes(2, 3)
- ones(5, 7)
- randn(2, 3)
When typing in X = A\b in Matlab to solve linear systems, which algorithm is used to solve it?
Gaussian elimination which is optimized for accuracy, but not efficiency
What happens to the error of the Matlab algorithm as N increases?
The error increases a great deal
When the lines are ________, the system Ax = b has no solution.
parallel
When the lines are ___________ each other, the system Ax = b has infinitely many solutions.
overlapping
When a Gaussian Elimination succeeds, we find a ______ solution to the linear system Ax = b.
unique
What is partial pivoting?
Partial pivoting is when you move the number with the largest magnitude to the pivot position before subtracting the rows below it to create zeroes.
What is the efficiency of Gaussian Elimination?
O(2/3n^3), for large n
What does the condition number of a matrix determine?
Kappa(A) measures how close to singular A is
When kappa(A) is large, A is ___-________
ill conditioned
How do you calculate kappa(A)?
||A||*||A^-1||
What is an example of an ill-conditioned matrix?
The Hilbert matrix
