Linear Transformation to Different Dimensions

Is the following transformation linear? T: R^3 -> R^2 defined by T(x,y,z)=(x,y)

Equivalence Classes

Question in attachment is as follows: Consider all lines in the plane. If a relationship between 2 lines is defined by the expression that their slopes are equal, prove that this relationship is an equivalence relationship. If we consider the set of all lines in the plane, how would you uniquely identify the equivalence clas ...continues

Proof - Natural Numbers

Prove the following conjectures, that for all N in the set of Natural Numbers... Question continued in attachment.

Proof Types

Describe the steps in and/or define how to accomplish the following types of proofs: a. That two sets are equal. b. That two sets are disjoint. c. A proof by contra-positive. d. A proof by contradiction. e. A proof by Mathematical Induction. (Question is repeated in attachment)

Proving-Conjectures

Proving Conjectures. Please see attachment.

Zero Product Property-Proof

Prove the Zero Producty Property in real numbers that: If ab=0 then a=0 or b=0 (Question is repeated in attachment)

Linear Algebra -- Vector Spaces -- Proofs

Show that C[a,b], with the usual scalar multiplication and addition of functions, satisfies the eight axioms of a vector space. Axioms: A1. x + y = y + x for any x and y in V. A2. (x + y) + z = x + (y + z) for any x,y,z in V. A3. There exists an element 0 in V such that x + 0 = x for each x in the set V. A4. For each x in ...continues

Linear Algebra -- Vector Spaces -- proofs

Let C be the set of complex numbers. Define addtion on C by (a + bi) + (c + di) = (a + c) + (b + d)i and define scalar multiplication by alpha(a + bi) = alpha*a + alpha*bi for all real numbers alpha. Show that C is a vector space with these operations. You'll have to prove the the Vector Space Axioms and the Closure Propertie ...continues

The Difference Between Standardized and Regular Regression Coefficient

I know that a standardized regression coefficient is able to provide us with a ranking of the relative importance of each independent variable in a regression model. However, I am confused about the difference between the standardized and regular regression coefficient. Can you help me distinguish the differences between t ...continues

Linear Algebra -- Vector Spaces

Let P be the set of all polynomials. Show that P, with the usual addition and scalar multiplication of functions, forms a vector space. Axioms: A1. x + y = y + x for any x and y in V. A2. (x + y) + z = x + (y + z) for any x,y,z in V. A3. There exists an element 0 in V such that x + 0 = x for each x in the set V. A4. Fo ...continues