Matrix, Inverse, Determinant - Advanced Engineering Math - Tutorial Slides, Slides of Engineering Mathematics

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Matrix, Inverse, Determinants

-^ Brief review^ •^ Matrix: Matrix Production and Properties^ •^ Inverse of a Matrix and its Properties^ •^ Determinant and its Properties^ •^ Matrix Related Matlab Functions •^ Drill problems and solutions •^ Q&A

Question 1: give examples to show that the followingproposition is wrong:ଶ^ 1, If^ ܣൌ Ͳǡ

then^ ܣൌ Ͳଶ (^) 2, If ܣܣ ൌ, then^ ܣൌ Ͳ^ or

3, If^ ܻܣ ൌ ܺܣ^

and^ Ͳ ്ܣ^ , then

ܺ ܻൌ docsity.com

Question 1: give examples to show that the followingproposition is wrong:ଶ^ 1, If^ ܣൌ Ͳǡ

then^ ܣൌ Ͳଶ (^) 2, If ܣܣ ൌ, then^ ܣൌ Ͳ^ or

3, If^ ܻܣ ൌ ܺܣ^

and^ Ͳ ്ܣ^ , then

Example:1, 2, 3,

Question 2: A,B are n*n symmetric matrices.Show: AB is symmetric matrix if and only if AB=BA.Proof:^ Sufficiency: If

, then so: Necessity: If^

, then so:

Matrix Related Matlab Functions >>A.^k>>A^k>>AB>>A.B>>inv(A)inverse of matrix A>>A'>>A(:,j)jth column of A>>A(:,m:n)>>A(i,m:n)>>[m n]=size(A)>>size(A,1)>>size(A,2)>>det(A)determinant of matrix A

>>fliplr(A)flip left and right of matrix A>>flipud(A)flip up and down of matrix A>>diag(A)>>diag(A,k)>>eye(n)>>eye(m,n)>>ones(n)>>ones(m,n)>>zeros(n)>>zeros(m,n)>>rank(A)rank of matrix A>>trace(A)trace of matrix A docsity.com