# Suppose that begin{bmatrix}4 & A & 2&4 -7 & -4 & -4 & B end{bmatrix} + begin{bmatrix}0 & 7& C&2 3 & D & 4 & -7 end{bmatrix}=begin{bmatrix}4 & 3 & 10&6 -4 & -5 & 0 & -4 end{bmatrix} What are the values of A,B,C and D ?

Suppose that $\left[\begin{array}{cccc}4& A& 2& 4\\ -7& -4& -4& B\end{array}\right]+\left[\begin{array}{cccc}0& 7& C& 2\\ 3& D& 4& -7\end{array}\right]=\left[\begin{array}{cccc}4& 3& 10& 6\\ -4& -5& 0& -4\end{array}\right]$
What are the values of A,B,C and D ?
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Step 1
Add the given matrices with their the corresponding elements,
$\left[\begin{array}{cccc}4& A& 2& 4\\ -7& -4& -4& B\end{array}\right]+\left[\begin{array}{cccc}0& 7& C& 2\\ 3& D& 4& -7\end{array}\right]=\left[\begin{array}{cccc}4& 3& 10& 6\\ -4& -5& 0& -4\end{array}\right]$
$\left[\begin{array}{cccc}4& A+7& 2+C& 6\\ -4& -4+D& 0& B-7\end{array}\right]=\left[\begin{array}{cccc}4& 3& 10& 6\\ -4& -5& 0& -4\end{array}\right]$
Step 2
If the two matrices are equal then their corresponding elements are also equal. The above two matrices are equal,
Thus,
$A+7=3⇒A=-4$
$2+C=10⇒C=8$
$-4+D=-5⇒D=-1$
$B-7=-4⇒B=3$
Jeffrey Jordon