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第2196题:principal submatrices



If AA is any n×nn \times n matrix, let (r)A{(r)} \atop A  denote the r×r r \times r submatrix in the upper left corner of A, that is (r)A {(r)} \atop A is the matrix obtained from AA by deleting the last nrn-r rows and columns. the matrics (1)A{(1)} \atop A , (2)A{(2)} \atop A , (3)A{(3)} \atop A ,  \cdots , (n)A {(n)} \atop A  are called the principal submatrices of AA .


If A=[1741221531162431]A= \begin{bmatrix} 1 & 7 & 4 & 1 \\ 2 & 2 & 1 & 5 \\ 3 & 1 & -1 & 6 \\ -2 & 4 & 3 & 1 \end{bmatrix}  then (3)A{(3)} \atop A =(  ).



A. [171225316]\begin{bmatrix} 1 & 7 & 1 \\ 2 & 2 & 5 \\ 3 & 1 & 6 \end{bmatrix} 



B. [174221311]\begin{bmatrix} 1 & 7 & 4 \\ 2 & 2 & 1 \\ 3 & 1 & -1 \end{bmatrix}



C. [741215116]\begin{bmatrix} 7 & 4 & 1 \\ 2 & 1 & 5 \\ 1 & -1 & 6 \end{bmatrix}



D. [221311243] \begin{bmatrix} 2 & 2 & 1 \\ 3 & 1 & -1 \\ -2 & 4 & 3 \end{bmatrix}

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