Help me to match the correct answer for each of the following situations. Plz~

[poon2009]

[h=1]Let T be an linear transformation from R^r to R^s. Let A be the standard matrix of T.?[/h] Let T be an linear transformation from R^r to R^s. Let A be the standard matrix of T.
Fill in the correct answer for each of the following situations.

1. The row-echelon form of A has a row of zeros.
2. Two rows in the row-echelon form of A do not have pivots.
3. The row-echelon form of A has a pivot in every column.
4. Every row in the row-echelon form of A has a pivot.

A. T is onto
B. T is not onto
C. There is not enough information to tell.

Thanks~

 

[Deleted member 4993]

Let T be an linear transformation from R^r to R^s. Let A be the standard matrix of T.?

Let T be an linear transformation from R^r to R^s. Let A be the standard matrix of T.
Fill in the correct answer for each of the following situations.

1. The row-echelon form of A has a row of zeros.
2. Two rows in the row-echelon form of A do not have pivots.
3. The row-echelon form of A has a pivot in every column.
4. Every row in the row-echelon form of A has a pivot.

A. T is onto
B. T is not onto
C. There is not enough information to tell.

Thanks~

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