Rank of a Matrix

Q.

What is the rank of matrices?

Q.

Match the following

$x+y+z=2$

$x+y+\lambda z=1$

$x+\mu y+2y=3$

(a) $\mu =1,\lambda =1$ (i) No solution

(b) $\mu =2,\lambda =3$ (ii) Unique Solution

(c) $\mu =1,\lambda =0$ (iii) Infinite Solutions

1. a-ii; b – iii: c- ii

2. a-i; b – ii: c- iii

3. a-iii; b – iii: c- i

4. a-i; b – iii: c- ii

Q.

The solution set the given set of equations will be

$x+y+z=6$

$x+2y+3z=10$

$x+2y+z=1$

1. Unique trivial solutions

2. Unique non trivial solution

3. No Solutions

4. Infinite solutions

Q. If $A=\left[\begin{array}{ccc}1& 0& 1\\ 0& 1& 2\\ 0& 0& 4\end{array}\right]$ and $|3A|=k|A|,$ then $k$ is

Q. The rank of the matrix $\left[\begin{array}{ccc}-1& 2& 5\\ 2& -4& a-4\\ 1& -2& a+1\end{array}\right]$ is

1. 1 if a = 6
2. 2 if a = 1
3. 3 if a = 2
4. 1 if a = -6

Q.

The Rank of the following matrix is

$\left[\begin{array}{cccc}1& 0& 0& 3\\ 0& 1& 1& 2\\ 0& 0& 0& 0\\ 0& 0& 1& 1\end{array}\right]-----------$

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