Determine whether the subset w ? v is a subspace

Reference no: EM13850797

In the following examples, determine whether the subset W ⊆ V is a subspace:

(a) V = F(R,R) is the R-vector space of all functions from R to R and W = {f : R → R | f (3) =-2} is the subset consisting of those functions f : R → R such that f (3) = -2;

(b) V = F(R,R) and W = {f : R → R | f (3) = 0}

.(c) V = R^2 and W ⊆ V is the subset consisting of those vectors (a,b) such that a^3 + b^5 = 0;

Reference no: EM13850797

Questions Cloud

What happens when c is a function of just one variable : What happens when C is a function of just one variable? Can you provide a geometric interpretation of what gradient descent is doing in the one-dimensional case?

Evaluate the strengths and weaknesses of the organizations : Evaluate the strengths and weaknesses of the organizations cybersecurity policy along attributes - Analyze the range of organizational policies (the policy framework) that are needed to effectively manage cybersecurity risks.

Pairs of vectors and describe it geometrically : 1. Determine the spans of the following pairs of vectors and describe it geometrically: (a) v1 = (1,-1,2), v2 = (2,-1,3) (b) w1 = (1,2,-1), w2 = (-5,-10,5)

Find a set of weights and biases for the new output layer : Find a set of weights and biases for the new output layer. Assume that the first 3 layers of neurons are such that the correct output in the third layer has activation at least 0.99, and incorrect outputs have activation less than 0.01.

Determine whether the subset w ? v is a subspace : In the following examples, determine whether the subset W ⊆ V is a subspace: (a) V = F(R,R) is the R-vector space of all functions from R to R and W = {f : R → R | f (3) =-2} is the subset consisting of those functions f : R → R such that f (3) = -2..

How much new total debt must the firm acquire : Cross Town Express has a sale of $137,000, net income of $14,000, total assets of $98,000, and total equity of $45,000. The firm paid $7,560 in dividends and maintains a constant dividend payout ratio. Currently, the firm is operating at full capacit..

Usual operations of addition and multiplication : Which of the following are vector spaces over R? Prove each answer. It may be helpfulin some cases to use what you know about subspaces .(a) The integers Z = {...,-2,-1,0,1,2,...} with the usual operations of addition and multiplication

What monthly car mortgage payments : What monthly car mortgage payments for the next 36 months are required to amortize a present loan of $3000 if interest is 12% compounded monthly?

How the architecture of neural networks plays a vital role : How The architecture of neural networks plays a vital role in classifying handwritten digits?

User Account

All Pages