Echelon Form of a Matrix

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. If $p\left(u\right)=4u^2+8u$. Find zeroes.

Q. Find the zero of x²-32x-105

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. Find the remainder when 11^120 divided by 75

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.