Question: Show that the matrix A + = (A T A) -1 A T which arises in the theory of the general linear model is a

Show that the matrix A⁺ = (A^TA)^-1A^T which arises in the theory of the general linear model is a generalized inverse of the (usually non-square) matrix A in that

(a) AAA = A (b) A+ AA+ A+ (c) (AA+) = AA+ (d) (A+A)T = A+ A.

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