Find |A| If `A = |(7x , 3), (5 , 6)|`

Answer

To find the determinant of the matrix \( A = \begin{pmatrix} 7x & 3 \\ 5 & 6 \end{pmatrix} \), we can follow these steps:

### Step 1: Write down the formula for the determinant of a 2x2 matrix.
The determinant of a 2x2 matrix \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is given by the formula:
\[ |A| = ad - bc \]

### Step 2: Identify the elements of the matrix.
In our case, we have:
- \( a = 7x \)
- \( b = 3 \)
- \( c = 5 \)
- \( d = 6 \)

### Step 3: Substitute the values into the determinant formula.
Now we can substitute the identified values into the determinant formula:
\[ |A| = (7x)(6) - (5)(3) \]

### Step 4: Perform the multiplication.
Calculating the products:
\[ |A| = 42x - 15 \]

### Step 5: Write the final answer.
Thus, the determinant of matrix \( A \) is:
\[ |A| = 42x - 15 \]

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