BE Mechanical Engineering Semester 1 (FE First Year) - University of Mumbai Question Bank Solutions for Applied Mathematics 1

Solve the following equation by Gauss Seidal method:

`10x_1+x_2+x_3=12`
`2x_1+10x_2+x_3-13`
`2x_1+2x_2+10x_3=14`

Investigate for what values of μ and λ the equations x+y+z=6, x+2y+3z=10, x+2y+λz=μ has
1) No solution
2) A unique solution
3) Infinite number of solutions. 

Investigate for what values of 𝝁 𝒂𝒏𝒅 𝝀 the equation x+y+z=6; x+2y+3z=10; x+2y+𝜆z=𝝁 have
(i)no solution,
(ii) a unique solution,
(iii) infinite no. of solution.

If `tan(x/2)=tanh(u/2),"show that" u = log[(tan(pi/4+x/2))] `

Using the encoding matrix `[(1,1),(0,1)]` encode and decode the messag I*LOVE*MUMBAI.

Using encoding matrix `[(1,1),(0,1)]`encode and decode the message

“ALL IS WELL” .