Answer the questions

1. a. Define degenerate and non-degenerate linear equation with example.


2. Solve the following systems of linear equation:-

3x1-x2+x3=-2

x1+5x2+2x3=6

2x1+3x2+x3=0

1. Find out the conditions on α, β and γ so that the following system of non-homogenous linear equations has a solution:-

x+2y-3z=α

3x-y+2z=β

2x-10y+16z=2γ

1. a. Write down the definition of the following matrices:-

1. Symmetric;


2. Skew symmetric


3. Nilpotent matrices.




1. If A and B are comparable matrices and At and Bt are the transpose matrices of A and B respectively then show that, (AB)t=BtAt.

1. Define sub-space of a vector space.


2. Let S be a non-empty sub-set of a vector space V then show that, <(S) is a sub-space of V containing S. furthermore, if W is any other sub-space of V containing S, then prove that, <(S) W.


3. Define linear dependence. Show that the non-zero vector v1, v2,……………. vn in a vector space v are linearly dependent if one of the vectors vk is a linear combination f the preceding vectors v1, v2,……………. Vk-1.


4. Determine a basis and the dimension for the solution space of the homogeneous system:-

x-3y+z=0

2x-6y+2z=0

3x-9y+3z=0

Group-B differential equation

• Define ordinary and particular differential equations with examples. Also define order and degree of a differential equation.