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determine whether W={(x,y,z)/ x+y+z+1=0, x,y,z element of real number} is a subspace of R^3 or not?
Let f(x)=4 g(x)=-4x+6 h(x)=2x^2+8x -3 inner product <p,q>=p(-1) q(-1) + P(0)q(0). +p(1)q(1) .usw gramschmidt to determine orthonormal basis for subspace p2 spanned by polynomials f(x) g(x) h(x)
The first four Hermite polynomials are f(x) = 1,g(x) = 2t, h(x) = 2−4t +t², and p(x) =
6−18t +9t²−t³
. Show that these polynomials form a basis for P3.
Let x, y and z be three vectors in a vector space V
a. Prove that the span{x,y, z} is a subspace of V.
Use the Gauss-Jordan process to determine for which value (s) of λ will the following system have no solutions?
"\\begin{bmatrix}\n 1 & 2 & -3 & 4\\\\\n 3 & -1 & 5 & 2\\\\\n 4 & 1 & \u03bb2 -14 & \u03bb +2\n\\end{bmatrix}"
Determine which of the following is the solution set of the linear equations below.
3x − y + z = 2
2x − z = 2
How is w=(3,5,1)∈R
3
a linear combination of u=(0,−2,2)
and v=(1,3,−1)
?
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
