Echelon Form of a Matrix

Q.

The Del factor for the reduction of number of microbial cells from 10¹⁰ to one is

1. $1$

2. $10$

3. $23$

4. $103$

Q.

A matrix is said to be in reduced Row echelon form if the leading 1 is the only nonzero entry in the row besides being in echelon form.

1. True

2. False

Q.

Which of the following conditions must a matrix satisfy for it to be in a row echelon form.

1. First non zero element of each row should be greater than 1

2. First non zero element of each row should be 1.

3. All zero rows should be on the top.

4. All non zero rows should be above all zero rows.

Q.

Which of the following is in reduced row Echelon form

1. $\left[\begin{array}{ccc}1& 0& 1\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

2. $\left[\begin{array}{ccc}1& 0& 0\\ 0& 0& 1\\ 0& 1& 0\end{array}\right]$

3. $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$

4. $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 0\end{array}\right]$

Q.

A matrix is said to be in reduced Row echelon form if the leading 1 is the only nonzero entry in the row besides being in echelon form.

1. True

2. False

Q. The entries of a matrix are integers. Adding an integer to all entries on a row or on a column is called an operation. It is given that for infinitely many integers N one can obtain, after a finite number of operations, a table with all entries divisible by N. Prove that one can obtain, after a finite number of operations, the zero matrix.

1. It is possible to obtain the zero matrix.
2. It is not possible to obtain the zero matrix.
3. The procedure will give identity matrix .
   
   
4. The procedure will give Skew-Symmetric matrix.

Q.

Which of the following is in reduced row Echelon form

1. 

2. 

3. 

4. 

Q.

Which of the following conditions must a matrix satisfy for it to be in a row echelon form.

1. First non zero element of each row should be greater than 1

2. First non zero element of each row should be 1.

3. All zero rows should be on the top.

4. All non zero rows should be above all zero rows.

Q. $\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 0\end{array}\right]$ is in reduced row Echelon form.

1. False
2. True

Q.

Which of the following conditions must a matrix satisfy for it to be in a row echelon form.

1. First non zero element of each row should be greater than 1

2. First non zero element of each row should be 1.

3. All zero rows should be on the top.

4. All non zero rows should be above all zero rows.