The vectors a and bare unit vectors such that a a+b and 2a +jb are perpendicular. --Determine the value of j such that the vectors

Make v3 a unit vector

Consider the set of vectors S= {u₁, U₂) in R³, where u₁ = (1,-1,2) and u₂ = (-2,0,3). Is the vector b= (12,-2, -11) a linear combination of the vectors in the set S? If it is, write b as a linear combination of u, and u₂. If it is not, explain why. Show all necessary calculations. Does the set S span R³? I in R², where Given the linear transformation T: R² R³ defined by T(x) = Ax for all x A = [u₁ U₂] 1-2 0 3 -1 2 does T map R² onto R³? Circle your choice below and briefly justify your answer. Circle One: [Onto / Not onto

Express the given vector in terms of the unit vectors i, j, and k. (14, 0, 4)