#### Find the value of A+C if $\\A+B=\left[\begin{array}{lll}{a+3} & {b+5} & {c+8} \\ {d+5} & {e+4} & {f+2} \\ {g+8} & {h+2} & {i+6}\end{array}\right]\\ \\\text{and}\\ \\B-C=\left[\begin{array}{lll}{a-1} & {b+3} & {c+4} \\ {d+2} & {e-4} & {f-1} \\ {g-5} & {h+1} & {i-3}\end{array}\right]\\$Option: 1 $A+C=\left[\begin{array}{lll}{2} & {8} & {12} \\ {7} & {0} & {1} \\ {3} & {3} & {3}\end{array}\right]$Option: 2 $A+C=\left[\begin{array}{lll}{4} & {2} & {4} \\ {3} & {8} & {3} \\ {13} & {1} & {9}\end{array}\right]$Option: 3 $A+C=\left[\begin{array}{lll}{4} & {2} & {4} \\ {3} & {0} & {3} \\ {13} & {1} & {9}\end{array}\right]$Option: 4 $A+C=\left[\begin{array}{lll}{2} & {8} & {12} \\ {7} & {8} & {1} \\ {3} & {3} & {3}\end{array}\right]$

Given,

$\\A+B=\left[\begin{array}{lll}{a+3} & {b+5} & {c+8} \\ {d+5} & {e+4} & {f+2} \\ {g+8} & {h+2} & {i+6}\end{array}\right]...........(1)\\ \\\text{and}\\ \\B-C=\left[\begin{array}{lll}{a-1} & {b+3} & {c+4} \\ {d+2} & {e-4} & {f-1} \\ {g-5} & {h+1} & {i-3}\end{array}\right]............(2)\\$

Now Subtract (2) from (1)

$\\(A+B)-(B-C)=\left[\begin{array}{lll}{(a+3)}-({a-1}) & {(b+5)-(b+3)} & {(c+8)-(c+4)} \\ {(d+5)-(d+2)} & {(e+4)-(e-4)} & {(f+2)-(f-1)} \\ {(g+8)-(g-5)} & {(h+2)-(h+1)} & {(i+6)-(i-3)}\end{array}\right]\\ \\ \\\Rightarrow A+C=\left[\begin{array}{lll}{4} & {2} & {4} \\ {3} & {8} & {3} \\ {13} & {1} & {9}\end{array}\right]$

Hence option (b) is correct.