consider the system of equations : ltbr. `3x-y +4z=3`
`x+2y-3z =-2`
`6x+5y+lambdaz =-3`
Prove that system of equation has at least one solution for all real values of `lambda`.also prove that infinite solutions of the system of equations satisfy `(7x-4)/(-5)=(7y+9)/(13)=z`

Explanation

To solve the given system of equations and prove the required conditions, we will follow these steps:

### Step 1: Write the system of equations in matrix form
The given equations are:
1. \( 3x - y + 4z = 3 \)
2. \( x + 2y - 3z = -2 \)
3. \( 6x + 5y + \lambda z = -3 \)

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