Compute det(aat) and det(a™a) for several randomly generated non-square matrices a e rmxn. you may use the following code several times on the command line in matlab. m = 4; n = 3; a = rand(m, n); detmbym = det(a * a'), detnbyn = det(a' + a) note here the command rand(m, n) generates a random mxn matrix with entries between 0 and 1, and the command det(a) calculates the determinant of a, and a' is the command that finds the transpose of a, at.
a. what happens when m is bigger than n?
b. what happens when n is bigger than m?
c. make a conjecture drawing a connection between invertible matrices and aat & at a where a e rmxn.
d. calculate the row reduce echelon form of aat and at a to support your conjecture. you may use the following commands. m= 4; n = 3; a = rand(m, n); rref_mbym =rref(a * a'), rref_nbyn = rref (a' + a) how is the size of the column space and the null space related to size of m and n?