Let v⃗ 1=⎡⎣⎢0−33⎤⎦⎥,v⃗ 2=⎡⎣⎢220⎤⎦⎥,v⃗ 3=⎡⎣⎢20−2⎤⎦⎥ be eigenvectors of the matrix A which correspond to the eigenvalues λ1=−3, λ2=0, and λ3=1, respectively, and let x⃗ =⎡⎣⎢−6−57⎤⎦⎥. Express x⃗ as a linear combination of v⃗ 1, v⃗ 2, and v⃗ 3, and find Ax⃗ .

Elijah and his sister went to the movies. they had $34 altogether and spent $9.50 per ticket. elijah and his sister bought the same snacks. write and solve an inequality fotlr the amount that each person spent on snacks. interpret the solition

For what value of x does 4x = (1/8) x + 5?

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."