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Consider the matrix A = X(XtX)^(-1)Xt. X has 5 rows and 3 columns. (Xt) means matrix...

Consider the matrix A = X(XtX)^(-1)Xt. X has 5 rows and 3 columns. (Xt) means matrix transpose of X.

Pick any 5x3 matrix for X (at least 9 of elements of X have to be different from 0 or 1). Your choice! Calculate A ( A - I ). (Hint the answer to this question is possibly much shorter than what you would expect!)

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Answer #1

X has 5 rows and 3 columns.

Let X be any general matrix (all elements different from 0 or 1).

Few properties to remember for matrix M and N

Using these properties, we get:

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