. Let A =     −2 −1 −1 2 1 0 0 2 5 3 0 3     . (a) Enter A into MATLAB and use MATLAB to compute the dot product of the first column of A with its second column. Also compute the dot product of the third column with itself. (See guide for how to extract a column from a matrix.) (b) Compute the matrix product AT A. (c) ? What is the relationship between the entries of AT A and the dot products of the columns of A? Make sure your answer is consistent with your computations. (d) ? What in general is the relationship between the entries of AAT and dot products of vectors associated to A? (e) Compute AAT and do at least two dot product computations to support your previous answer. (f) Let Q =   1/ √ 14 1/ √ 3 5/ √ 42 2/ √ 14 1/ √ 3 −4/ √ 42 3/ √ 14 −1/ √ 3 1/ √ 42  . Do a single matrix computation which shows that the columns of form an orthonormal set. (g) ? Explain carefully why your computation above shows that the columns form an orthonormal set. (h) ? Explain why the rows of Q must also form an orthonormal set.