Find a formula for the least squares solution of ax=b when the columns of a are orthonormal1 .

Let be a rectangular matrix with column vectors , i.e.



Then we have



and the product of the two is



Because the columns of are orthonormal, we have



which means reduces to an matrix with ones along the diagonal and zero everywhere else, i.e.



where denotes the identity matrix. This means the solution to is given by

Ithink it’s b, hope this .

Multiply 9 and 67. then multiply 3 with 67. lastly the answer that you got for 9x67 is to be subtracted by the answer you got for 3x67