Answer TRUE or FALSE. x = 0 is a solution of the linear system Ax = b when b = 0

Question

Answer TRUE or FALSE. x = 0 is a solution of the linear system Ax = b when b = 0. A basic variable of a linear system Ax = b is a variable that corresponds to a pivot column of the augmented matrix Ab. A basic variable of a linear system Ax = b is a variable that corresponds to a pivot column of the coefficient matrix A. A free variable of a linear system Ax = b is a variable that corresponds to a column of the coefficient matrix A that is not pivot column. Whenever a consistent system Ax = b has free variables, then the system has Infinitely many solutions. x = 0 is not a solution of the linear system Ax = b when b notequalto 0.

Explanation / Answer

A basic variable in a linear system is a variable that corresponds to a pivot column in the coefficient matrix.

So, 1 ) False and 2) True

If a column of the coefficient matrix is not a pivot column, the corresponding variable is free and the system

of equations has a nontrivial solution

3) True.

Whenever a consistent system Ax= b has free varibles then the system has infinitely many solutions: 4) True

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