Problem3 State whether each statement is Trae or False, and justify your answer

Question

Problem3 State whether each statement is Trae or False, and justify your answer a. The reduced echelon form of a matrix is unique b. If every column of a an augmented matrix is a contains a pivot then the corresponding system is consistent. e. The pivot positions in a matrix depend on whether or not interchanges are used in the row reduction process d. A general solution of a system is an esxplicit description of all solutions of the system. e. Whenever a system has free variables, the solution set hasany slutions. Problem 4. The vectors u,v, w.x. y, z are given in the accompanying figure. Write each of the vectors w, x. y. z as linear combinations of the vectons u and v 2v 2v

Explanation / Answer

1) TRUE

all the reduced row echelon form have the same number of zero rows and the pivots are located in the same indices.

b) FALSE

The system is inconsistent if [A b] has a pivot in the last ("b") column. The system is consistent if the matrix A has a pivot in every row.

c) FALSE

Since the reduced row echelon form of A is unique, the pivot positions are uniquely determined and do not depend on whether or not interchanges are performed in the reduction process.

d) TRUE

it defines all the solutions of the sysytem.

e) False

A matrix may contain a free varible and still be inconsistence.

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