Algebra : Simplify

x^2+xy-2y^2/x^2+4xy+4y^2/(x^2-y^2) Numerator---Denominator

Algebra : Simplify

[(x^2+xy-2y^2)/x^2 + (4xy+4y^2)]/[(x^2-y^2)]

Vectors and Linear Algebra : Basis, Column Space and Rank

2 1 -1 3 4 1 0 -1 2 0 A= 1 1 0 1 4 4 2 -2 6 8 Find the basis for the row space, column space of A; What is the rank of A?

5 Problems: Logarithmic, Exponential, Solve Equation, Inequality

Five problems are "solved for x".

A Function of Years

D(x) is the number of days in the year x. Leap years have 366 days. Others have 365 days. D(1980)= D(1950)= D(1776)= This is three of our problems. How do we calculate these equations? The above info is all that is given.

Linear alegbra

Consider the following elements of the vector space P3 of all polynomials of degree less than or equal to 3. p(x)= x-1, q(x)=x+x2, r(x)= 1+x2-x3 Do these three polynomials form a basis for P3?

Linear Alegbra and Vectors : Linear Dependence

Determine whether or not the following set of vectors in R4 is linearly independent? u=(1,0,3,0) v=(2,1,1,3) w=(1,2,-7,6)

Linear equation

Consider the equation Ax=b, with a=(1 1 a) (1 -1 1) (2 -1 -1) b=(6+b) ( b ) ( b ) for which values of a,b this system has no solutions? infinitely many solutions? unique solution? if possible, find the solution x explicitly in terms of a,b.

Matrix subspace

Consider the matrix a=(1 1 2 1 2 -1 3 2 1 5 5 2) Find N(A), R(A), N(A^T),R(A^T). Show that the fundamental subspace theorem holds: N(A^T)=R(A)^(upside down T), N(A)=R(A^T)^(upsidedown T). Hint: Notice that the fourth row is the sum of the first three rows.

Linear algebra

Suppose S is a linear space defined below. Are the following mappings L linear transformations from S into itself? If answer is yes, find the matrix representations of formations (in standard basis): (a) S=P4, L(p(x))=p(0)+x*p(1)+x^2*p(2)+X^3*p(4) (b) S=P4, L(p(x))=x^3+x*p'(x)+p(0) (c) S is a subspace of C[0,1] formed by ...continues