Linear Algebra Answers

Check whether the set of vectors {1 + 𝑥, 𝑥 + 𝑥2

, 1 + 𝑥3

} is a linearly independent set of

vectors in P3

, the vector space of polynomials of degree ≤ 3

Ali wants to surprise his wife Sara by presenting her some flowers, when he returns back from a work tour. He plans to spend exactly $24 on a bunch of exactly two dozen flowers. Sara loves lilies, roses and daisies. At the flower market they are selling lilies for $3 each, roses for $2 each, and daisies $0.50 each. How many flowers of each type can Ali buy? 

Find all values of lambda such that ,the following system has a none-zero solutions.

2x+y= lambda x

4x-y =lambda y

Determine whether the vector (9,0,9) is a linear combination of the vectors

(1,1,0), (1,0,1), (2,1,1) and (0,1, −1).

Let W = {(x, y, z): y² = x + z}, Is W a subspace of R³