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Competitive Stats
Q54Section I (Objective (Q1–Q80))54 of 80

Linear Algebra — rank and trace identities for a given matrix

If A=[223 101 324]A = \begin{bmatrix} 2 & 2 & 3 \ 1 & 0 & 1 \ 3 & 2 & 4 \end{bmatrix} and A−A^- denotes the generalized inverse of AA, then consider the following statements: I. Rank (A)=2(A) = 2 II. Trace (A−A)=2(A^-A) = 2 III. Trace (AA−)(AA^-) = Trace (A−A)(A^-A) IV. Trace (A)=6(A) = 6 How many of the statements given above are correct?

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