(a). Consider the Over-determined system Σakjxj = bk, j=0 n 0≤k ≤m, In general, since the number of equations m + 1 is l

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(a). Consider the Over-determined system Σakjxj = bk, j=0 n 0≤k ≤m, In general, since the number of equations m + 1 is larger than the number of unknown n+1, the system has no solutions. A "best solution" can be defined as the one that minimizes the error Derive the normal equations. m n ψ(20,21,...,Xn) = ΣΙΣanja; bk j=0 n <m. k=0 (c). Now, expression the system in matrix-vector form Ax = b 2 (b). Determine the “best solution" (in the least square sense) for the following system 2x + 3y = 1, x- - 4y = -9, 2x - y = -1. where A is a rectangular matrix, which has more rows than columns. Show that the normal equations can be written as (ATA)x= ATb.