Let x1 =, x2 =, xz = . a. show that these vectors are linearly independent. b. write v = as a linear combination of these vectors. (1 -1 01 72 -1 2

Write the sentence as an equation. 6 fewer than the quantity 140 times j equals 104

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

What can each term of the equation be multiplied by to eliminate the fractions before solving? x – + 2x = + x 2 6 10 12