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(Solved) Given two 3*4 matrix M and M', M = [A,b], M' = [A', b']. A and A' are 3*3 invertible matrix, b and b' are 3*1 matrix. Also assume e t (-A T A -1 b +...


Given two 3*4 matrix M and M', M = [A,b], M' = [A', b']. A and A' are 3*3 invertible matrix, b and b' are 3*1 matrix.

Also assume et(-ATA-1b + b') !=0, where et = [0,0,1]t.

M_hat = [I3*3, 03*1], M_hat' = [m11*4, m21*4, [0,0,0,1]] where m1 and m2 are any 1*4 matrix.

Show that there is a 4*4 matrix H such that MH = M_hat and M'H = M_hat'.


Hint is to decompose H into H0 and H1 such that MH0 = M_hat. After find H0, then find H1, so that M'H0H1 = M_hat' and also keep MH0H1 = M'.

 


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