Determine if the statement is true or false:

1. if two matrices are equivalent, then one can be transformed into the other with a sequence of elementary row operations.
2.different sequences of row operations can lead to different echelon forms for the same matrix.
3.different sequences of row operations can lead to different reduced echelon forms for the same matrix.
4.if a linear system has four equations and seven variables, then it must have infinitely many solutions.

Exercise: counting committees 0.0/2.0 puntos (calificable) we start with a pool of n people. a chaired committee consists of k≥1 members, out of whom one member is designated as the chairperson. the expression k(nk) can be interpreted as the number of possible chaired committees with k members. this is because we have (nk) choices for the k members, and once the members are chosen, there are then k choices for the chairperson. thus, c=∑k=1nk(nk) is the total number of possible chaired committees of any size. find the value of c (as a function of n ) by thinking about a different way of forming a chaired committee: first choose the chairperson, then choose the other members of the committee. the answer is of the form c=(α+nβ)2γn+δ. what are the values of α , β , γ , and δ ?