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.

Question

Aleena Cantrell

Mathematics

1 December, 22:12

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.

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Answers (1)

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Francis Flores · Answer 1

Step-by-step explanation:

given are four statements and we have to find whether true or false.

.1 If two matrices are equivalent, then one can be transformed into the other with a sequence of elementary row operations.

True

2. Different sequences of row operations can lead to different echelon forms for the same matrix.

True in whatever way we do the reduced form would be equivalent matrices

3. Different sequences of row operations can lead to different reduced echelon forms for the same matrix.

False the resulting matrices would be equivalent.

4. If a linear system has four equations and seven variables, then it must have infinitely many solutions.

True, because variables are more than equations. So parametric solutions infinite only is possible