1) Select the correct statements from below for a linear system of equations Ax = b

a) The determinant of a permutation matrix is negative if it leads to an odd number of row interchanges in Gaussian elimination.

b) A zero in the pivot position upon pivoting implies that the matrix A is singular

c) If A is a lower triangular matrix, then the system could be solved by back-substitution

d) The number of floating point operations in back-substitution is of order

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