Find an example of 4 linearly independent vectors a₁, a₂, a₃, a₄ ∈ R 4 such that the linear transformation T : R 4 → R 4 , T(x) = x₁a₁ + x₂a₂ + x₃a₃ + x₄a₄ is not onto, OR explain why this is not possible. If you provide an example, your answer should include an explanation of why those vectors have the desired properties.

Anew test for ra is being developed. the test is administered to 750 patients with ra and 750 without ra. for the sake of the question, assume the prevalence of ra in this population is 50%. of the 750 patients with ra, 575 have a positive result. of the 750 patients without ra, 150 have a positive result. what is the positive predictive value of the new test? a575/(575+150) b. 600/(600+ 150) c. 575/(575+125) d. 600/(600+ 125)