Applying KVL to Mesh 1, 

$12-12I_1-10(I_1-I_2)-1(I_1-I_3)=0\\ 13I_1-10I_2-I_3=12........................(1)$

Applying KVL to Mesh 2, 

$-10(I_2-I_1)-10-2I_2-3(I_2-I_3)=0\\ -10I_1+15I_2-3I_3=0..........................(2)$

Applying KVL to Mesh 3, 

$1(I_3-I_1)-3(I_3-I_2)-4I_3+24=0\\ -I_1-3I_2+8I_3=24.....................................(3)$

Writing equations in the matrix form

$\left[\begin{matrix} 13&-10&-1 \\ -10&15&-3\\ -1&-3&8 \end{matrix}\right] \left[\begin{matrix} I_1\\ I_2\\ I_3 \end{matrix}\right]= \left[\begin{matrix} 12\\ -10\\ 24 \end{matrix}\right]$

Solving above equations we get, 

$I_1=2.79\ A;\\ I_2=2.01\ A;\\ I_3=4.1\ A; \\ I_{4 \Omega }=I_3=4.1\ A$