MATLAB4 - MATH20F|EdwardChang|A09415574|MaxMetti|MATLAB

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 20F | Edward Chang | A09415574 | Max Metti | MATLAB  Assignment 4 | CO1: 10:00AM Eigenvalues, Determinants and Diagonalization EXERCISE 4.1 (A) >> A = [8, 11, 2, 8; 0, -7, 2, -1; -3, -7,  2, 1; 1, 1, 2, 4] A =      8    11     2     8      0    -7     2    -1     -3    -7     2     1      1     1     2     4 >> B = [1, -2, 0, 5; 0, 7, 1, 5; 0, 4, 4, 0;  0, 0, 0, 2] B =      1    -2     0     5      0     7     1     5      0     4     4     0      0     0     0     2 >> A+B ans =      9     9     2    13      0     0     3     4     -3    -3     6     1      1     1     2     6 >> A-B ans =      7    13     2     3      0   -14     1    -6     -3   -11    -2     1      1     1     2     2 >> A*B ans =      8    69    19   111      0   -41     1   -37     -3   -35     1   -48      1    13     9    18 >> inv(A) ans =     0.4211    0.0526    0.4737   -0.9474    -0.4474    0.1316   -0.8158    1.1316    -1.2500    0.7500   -2.2500    3.2500 0.6316   -0.4211    1.2105   -1.4211 >> B' ans =      1     0     0     0     -2     7     4     0      0     1     4     0      5     5     0     2 EXERCISE 4.1 (B) Matrix A+B is NOT invertible because the det(A+B) = 0 (Known through using  MATLAB)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
>> det(A+B) ans =      0 EXERCISE 4.1 (C) Knowing the determinants of A and B will allow us to recover the determinants of: , = detAB becausedetAB detAdetB - , - = detA 1 becausedetA 1 1detA , = ( ) anddetBT becausedetBT det B , ± , ± ≠ ± However it WILL NOT tell usdetA B becausedetA B detA detBcommon error EXERCISE 4.2 >> N = [0.02, 0.003, 0; 1, 0.01, 0; 0, 0, 0.005] N =     0.0200    0.0030         0     1.0000    0.0100         0          0         0    0.0050 >> det(N^100) ans =      0 >> det(N) ans =  -1.4000e-005 Question: Do you think that  N100  is invertible?  Yes, because the numbers will become too small for MATLAB to estimate as numbers, so  it rounds all these numbers to 0, and thus it calculates that the determinant is 0. Calculation by hand: = =- . - , detN100 detN100 1 4000e 005100 by hand as far as we can go
Background image of page 2
Just an intellectual search, using WolframAlpha’s powerful engine: - . - = . - 1 4000e 005100 4 10019e 486 Question: Would you now reconsider your answer to the previous question?  Explain. Yes. We can therefore see that det(N
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/17/2011 for the course MATH 20F taught by Professor Buss during the Winter '03 term at UCSD.

Page1 / 10

MATLAB4 - MATH20F|EdwardChang|A09415574|MaxMetti|MATLAB

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online