Row Echelon Form

Q. The rank of the matrix $\left[\begin{array}{ccccc}1& -1& 0& 0& 0\\ 0& 0& 1& -1& 0\\ 0& 1& -1& 0& 0\\ -1& 0& 0& 0& 1\\ 0& 0& 0& 1& -1\end{array}\right]$ is ____.

1. 4

Q. The rank of matrix A = $\left[\begin{array}{ccc}1& 2& 3\\ 3& 4& 5\\ 4& 6& 8\end{array}\right]$ is

1. 0
2. 1
3. 2
4. 3

Q. Given matrix $\left[A\right]=\left[\begin{array}{cccc}4& 2& 1& 3\\ 6& 3& 4& 7\\ 2& 1& 0& 1\end{array}\right]$. The rank of the matrix is _____ .

1. 4
2. 3
3. 2
4. 1

Q. The rank of the matrix $\left[\begin{array}{cccc}1& 4& 8& 7\\ 0& 0& 3& 0\\ 4& 2& 3& 1\\ 3& 12& 24& 2\end{array}\right]$

1. 3
2. 1
3. 2
4. 4

Q. The rank of the matrix$A=\left[\begin{array}{cccc}1& 2& -1& 3\\ 4& 1& 2& 1\\ 3& -1& 1& 2\\ 1& 2& 0& 1\end{array}\right]$ is

1. 3
2. 1
3. 2
4. 4

Q. The rank of the matrix $A=\left[\begin{array}{ccc}1& -2& -1\\ -3& 3& 0\\ 2& 2& 4\end{array}\right]$ is

1. One
2. Two
3. Three
4. None of the above

Q. The rank of the matrix $\left[\begin{array}{ccccc}1& -1& 0& 0& 0\\ 0& 0& 1& -1& 0\\ 0& 1& -1& 0& 0\\ -1& 0& 0& 0& 1\\ 0& 0& 0& 1& -1\end{array}\right]$ is ____.

1. 4

Q. The rank of the matrix, $A=\left[\begin{array}{ccc}0& 1& 1\\ 1& 0& 1\\ 1& 1& 0\end{array}\right]$is

1. 0
2. 1
3. 2
4. 3

Q.

Find the literal factor and numerical factor from the following.

$-32x^3{y}^{3}z$

Q. Let A be a 4 $\times$ 3 real matrix with rank 2. Which one of the following statement is TRUE?

1. Rank of $A^{T}A$ is less than 2
2. Rank of $A^{T}A$ is equal to 2
3. Rank of $A^{T}A$ is greater than 2
4. Rank of $A^{T}A$ can be any number between 1 and 3