1. This problem is about linear independence and dependence. Let S= {₁, 2, 3) be a subset of R¹. (a) Explain how to show whether the set S is linearly independent or linearly dependent using the algebraic definition. (b) Discuss how to determine whether the set S is linearly independent or linearly dependent using the geometric viewpoint. (c) Suppose the set S is linearly independent. Explain how to find a vector 4€ R¹ so that T = {₁, U2, U3, U4} is linearly independent.

Please solve this linear algebra problem with a good explanation.

§7. (6 p) Let each set S1, S2 be formed by only one vector: S₁ Is S₁ LI, LD or neither? Is S₂ LI, LD or neither? Is the set { , } LI, LD or neither? = { 7 }, S₂ = { 0

The vector y is a numerical vector. Which ONE of the following best describes what the R code below will calculate?   sum(!is.na(y)) A logical vector of the same length as the vector y, which takes the value TRUE for values in y which are NOT missing and FALSE for values in y which ARE missing.   Replaces each value in y with TRUE if it is not missing and FALSE if it is missing   The number of non-missing values in the vector y.   The number of missing values in the vector y.   The propostion of non-missing values in the vector y.