Please write your solutions clearly and neatly. Justify them completely.
• Fill out your name and Section below.• Upload your solutions (including this cover page) to Gradescope before the deadline. where a is a scalar.
(a) For what values of a does the matrix A have rank less than 3 What is its rank in those cases.(b) (5 points) Find a value of the scalar a and a vector ~b ∈ R 3
such that the equation
A~x = ~b
has no solutions. Explain your answer.
You are also given that one of them is a rotation, one is a reflection about a line (passing through the origin) and one is an orthogonal projection. Being the resident linear algebra detective, it is your job to find out which one is which, and deduce as much about them as possible.What can you infer at this point and why?
(b) You find out next that What can you infer now and why? Be as detailed as is possible. (c) Finally, you find out that.Using this and all of the information above, find TRUE or FALSE? Justify your answers.(a) There exists a 4 × 3 matrix A of rank 3.