Linear Algebra Answers

Let V = set of all 3x1 matrices.

Define

+ to be the matrix addition

⦁ to be the matrix multiplication by a number

We know that V is a vector space. If W [a, b, 1] , a, b element of R then W is a subspace of V.

Let V be the set of all positive real numbers; define + by u+v = uv (+ is ordinary multiplication) and define • by c•v = . Prove that V is a vector space.

1. For what values of h the vectors

⟶ [ 1 ⟶ [ -1 ⟶ [ 5

u = -3 u_{2 =} 9 u₃ = -7 <--- u₁, u₂, and u₃ are vectors

-2] -6] h]

are linearly independent?

 Doctors have become increasingly concerned about the sodium intake in the U.S. diet. Recommendations by the American Medical Association indicate that most individuals should not exceed 2400 mg of sodium per day. Liza ate 1 slice of pizza, 1 serving of ice cream, and 1 glass of soda for a total of 1030 mg of sodium. David ate 3 slices of pizza, no ice cream, and 2 glasses of soda for a total of 2420 mg of sodium. Melinda ate 2 slices of pizza, 1 serving of ice cream, and 2 glasses of soda for a total of 1910 mg of sodium. How much sodium is in one serving of each item?

Restriction: Use matrix inversion to answer to this question)

(1,2,-1,0),(1,3,1,2), (4,2,1,0), (6,1,0,1) examine whether the following vectors are linearly independent or dependent.

V =((x,y,0)T ∈R3 :x,y∈R).Using the definition of the subspace, show that V is a subspace of the vector space R3.Using the definition of the subspace, show that V is a subspace of the vector space R3.

Find Elementary matrices E1, E2 so that E2 E1 A = I2, where A = matrix(1 0 2 3) and I2 is the respective identity matrix

Find a basis and the dimension of the subspace W of ℝ^3 where W = {( x, y, z ) ∈ ℝ^3 ∶ x + y + z = 0 }.

Determine the subspace of ℝ^3 spanned by the vectors α = 1, 2, 3 , β = 3, 1, 0 . Examine whether

γ = 2, 1, 3 , δ = (−1, 3, 6) are in the subspace or not.

To ensure a growing season of sufficient length, Mang Popoy has at most 16 days left to

plant corn and soybean . he can plant com at a rate of 10 hectares per day and soybean at

15 hectares per day. If he has at most 200 hectares available, how many hectares of each

type of crop can he plant?​