1.3

Every matrix can be transformed into a unique matrix in row echelon form by a sequence of elementary row operations.

False

Every system of linear equations has at least one solution.

False

If a system of linear equations has more variables than equations, then it must have infinitely many solutions.

False

If A is the coefficient matrix of a system of m linear equations in n variables, then A is an n x m matrix.

False. A = m x n.

Multiplying every entry of some row of a matrix by a scalar is an elementary row operation.

False. By a non-zero scalar.

Some system of linear equations have exactly two solutions.

False. Every system of linear equations has exactly one solution, no solution or infinite number of solutions.

A system of linear equations Ax = b has the same solutions as the system of linear equations Rx = c, where [R c] is the reduced row echelon form of [A b].

True

A system of linear equations is called consistent if it has one or more solutions.

True

Every matrix can be transformed into a unique matrix in reduced row echelon form by a sequence of elementary row operations.

True

Every matrix can be transformed into one in reduced row echelon form by a sequence of elementary row operations.

True

Every solution of a consistent system of linear equations can be obtained by substituting appropriate values for the free variables in its general solution.

True

If A is an m x n matrix, then a solution of the system Ax = b is a vector u in R^n such that Au = b.

True

If a matrix A can be transformed into a matrix B by an elementary row operation, then B can be transformed into A by an elementary row operation.

True

If the only non-zero entry in some row of an augmented matrix of a system of linear equations lies in the last column, then the system is inconsistent.

True

If the reduced row echelon form of the augmented matrix of a consistent system of m linear equations in n-variables contains k-nonzero rows, then its general solution contains k-basic variables.

True