If `[(3,-2),(5,6)]+2A=[(5,6),(-7,10)]` then A=?

Options

A. `[(1,3),(-5,4)]`
B. `[(1,5),(-3,4)]`
C. `[(1,4),(6,2)]`
D. none of these

Explanation

To solve the equation \([(3,-2),(5,6)] + 2A = [(5,6),(-7,10)]\), we will follow these steps:

### Step 1: Isolate \(2A\)
We start with the equation:
\[ [(3,-2),(5,6)] + 2A = [(5,6),(-7,10)] \]
To isolate \(2A\), we subtract \([(3,-2),(5,6)]\) from both sides:
\[ 2A = [(5,6),(-7,10)] - [(3,-2),(5,6)] \]

### Step 2: Perform the subtraction
Now, we perform the subtraction element-wise:
\[ [(5-3), (6-(-2))] = [(2), (6+2)] = [(2), (8)] \]
\[ [(-7-5), (10-6)] = [(-12), (4)] \]
Thus, we have:
\[ 2A = [(2, 8), (-12, 4)] \]

### Step 3: Divide by 2 to find \(A\)
Now, we divide each element of the matrix \(2A\) by 2 to find \(A\):
\[ A = \frac{1}{2} \cdot [(2, 8), (-12, 4)] = [(1, 4), (-6, 2)] \]

### Final Answer
Thus, the matrix \(A\) is:
\[ A = \begin{pmatrix} 1 & 4 \\ -6 & 2 \end{pmatrix} \]

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