Problem

Given the following matrices, if possible, determine $A+B+C$. If not, state "Not Possible".
\[
A=\left[\begin{array}{cc}
-4 & 8 \\
0 & 0 \\
-5 & -2
\end{array}\right] \quad B=\left[\begin{array}{cc}
-5 & -10 \\
-5 & -5 \\
6 & 5
\end{array}\right] \quad C=\left[\begin{array}{cc}
9 & -3 \\
3 & -5 \\
-9 & 0
\end{array}\right]
\]

Answer

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Answer

Final Answer: \(\boxed{\begin{array}{cc} 0 & -5 \\ -2 & -10 \\ -8 & 3 \end{array}}\)

Steps

Step 1 :We are given three matrices A, B, and C, and we are asked to find the sum of these matrices, if possible.

Step 2 :The operation of adding matrices is possible if and only if the matrices have the same dimensions. In this case, all matrices A, B, and C are 3x2 matrices, so the addition is possible.

Step 3 :The result of the addition will be a new 3x2 matrix where each element is the sum of the corresponding elements in matrices A, B, and C.

Step 4 :Matrix A is \[\begin{array}{cc} -4 & 8 \\ 0 & 0 \\ -5 & -2 \end{array}\]

Step 5 :Matrix B is \[\begin{array}{cc} -5 & -10 \\ -5 & -5 \\ 6 & 5 \end{array}\]

Step 6 :Matrix C is \[\begin{array}{cc} 9 & -3 \\ 3 & -5 \\ -9 & 0 \end{array}\]

Step 7 :The sum of matrices A, B, and C is \[\begin{array}{cc} 0 & -5 \\ -2 & -10 \\ -8 & 3 \end{array}\]

Step 8 :Final Answer: \(\boxed{\begin{array}{cc} 0 & -5 \\ -2 & -10 \\ -8 & 3 \end{array}}\)

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