Rank of a Matrix

Q.

$\left[\begin{array}{ccc}3& -1& 2\\ -3& 1& 2\\ -6& 2& 4\end{array}\right]$What is the rank of the matrix.

1. 1

2. 2

3. 3

4. 4

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.

If matrix is in Row Echelon form then the Rank is equal to number of non zero rows.

1. True

2. False

Q.

Given A and C are coefficient and augmented matrices respectively for a system of linear equations. Which of the following cases tells if the equations are consistent?

1. Rank of A > Rank of C

2. Rank of A < Rank of C

3. Rank of A = Rank of C

4. None of these

Q.

The Rank of the following matrix is

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

__

Q.

Which of the following is true if A and C are coefficient and augmented matrices respectively for a system of linear equation. Here n = number of unknowns

1. Rank A = Rank of C=n, Infinite solutions

2. Rank A = Rank of C = r, r < n, Infinite solutions

3. Rank A = Rank of C = n, unique solution

4. Rank A = Rank of C = r< n, unique solution

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