In this problem, the submatrix of A is A2. A2 is the submatrix that forms after apply Gaussian elimination to the first column of A, so A2 is the submatrix that excludes row 1 and column 1 of A after Gaussian elimination.
Clarification:The matrix it's referring to is A2. A2 was created after Gaussian elimination was applied to only the first column of A. So this yields.the matrix [a11 a1^t; 0 A2]. a1^t is the rest of the first row. Everything below a11 in column 1 is zero. Then A2 is the submatrix.