MAT 335

Main Topics for Test 2

Wednesday, Oct. 24, 2007

Sections 1.10, 2.1-2.3, 2.5, 3.1, 3.2

Matrix operations

Be able to:

• perform matrix addition, scalar multiplication, matrix multiplication, and matrix transpose

• find the inverse of a matrix by the "augmentation method"

• properly use properties of matrix addition, scalar multiplication, matrix multiplication, the transpose, and the inverse

• solve a given matrix equation for a certain matrix

• use entry-by-entry notation to prove properties of matrix addition and scalar multiplication

• properly use the Invertible Matrix Theorem

Applications

Be able to:

• set up and solve systems to find current in electrical networks

• set up and solve systems to find food mixtures providing desired nutrients

• set up and use migration matrices to analyze population movement

• find the LU-factorization of a matrix (by hand or with MATLAB's gauss)

• use the LU-factorization of A to solve Ax=b (by hand or with MATLAB)

Determinants

Be able to:

• find the determinant of a matrix by the cofactor expansion method

• find the determinant of a matrix using the effect of elementary row operations on the determinant, and by various short-cuts

• test for invertibility of a matrix using the determinant

• use the properties that det(AB) = det(A) det(B) and det(A^T) = det(A)

Miscellaneous

Be able to:

• answer true/false questions about the concepts mentioned on this page

MATLAB use

Be able to use MATLAB to:

• make computations in population movement problems

• implement the method of finding the inverse of A by the augmentation method

• make the necessary computations to find and use LU factorizations