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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.
A construction company manufactures bags of concrete mix from beach sand and river sand. Each cubic of gravel. Each cubic meter of river sand costs P100 and contains 3 units of fine sand, 6 units of coarse sand, and 2 units of gravel. Each bag of concrete must contain at least 12 units of fine sand, 12 units of coarse sand, and 10 units of gravel. Find the best combination of beach and river sand which will meet the minimum requirements of fine sand, coarse sand, and gravel at the least cost.
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?
#339914 on Dec 2023