For the OLS Estimator $\hat { \beta}$ = $X ^ { \prime }$

question 33

Essay

For the OLS estimator $\hat { \beta}$ = ( $X ^ { \prime }$ X)^-1
$X ^ { \prime }$ Y to exist, X'X must be invertible. This is the case when X has full rank. What is the rank of a matrix? What is the rank of the product of two matrices? Is it possible that X could have rank n? What would be the rank of X'X in the case n<(k+1)? Explain intuitively why the OLS estimator does not exist in that situation.

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