Let v₁ = (2,-3,7,8), v2 = (3, 10, -6, 14), v3 = (0, 19, -2, 16), and v₁ = (9, -2, 1, 10). Is the set {V1, V2, V3, V4} a basis for R4? Of the two sets S = {(3x-5y, 4x + 7y, x+9y): x, y = R} and T = {2x-3y+z, -7x-3y²+z, 4x + 3z): x, y, z = R} which is a subspace of R3? (S, T, both, neither) Justify.

Find a basis and dimension for the null space of the following matrix: 3 -2 0 7 -2 1-1 1 5 3 19-2 8 06 1 -2 -4 -5-6 -9 4-6 11 6 Find a basis and dimension for the column space of the same matrix (above).

No chatgpt pls will upvote

No chatgpt pls will upvote

not use ai please

not use ai please

please answer the questions below ands provide the required codes in PYTHON. alsp provide explanation of how the codes were executed. Also make sure you provide codes that will be able to run even with different parameters as long as the output will be the same with any parameters given. these questions are not graded. provide accurate codes please

Could you please help me answer the follwoing questions

What is Poisson probability? What are 3 characteristics of Poisson probability?  What are 2 business applications of Poisson probability?  Calculate the Poisson probability for the following data. x = 3, lambda = 2 x = 2, lambda = 1.5 x = 12, lambda = 10 For the problem statements starting from question 6 onward, exercise caution when entering data into Microsoft Excel. It's essential to carefully evaluate which value represents x and which represents λ.  A call center receives an average of 3 calls per minute. What is the probability that exactly 5 calls are received in a given minute?  On average, 4 patients arrive at an emergency room every hour. What is the probability that exactly 7 patients will arrive in the next hour?  A production line produces an average of 2 defective items per hour. What is the probability that exactly 3 defective items will be produced in the next hour?  An intersection experiences an average of 1.5 accidents per month. What is the probability that…