Question

Find the value of the following determinant:
\[ \begin{vmatrix} 4 & 3 \\ 2 & 7 \end{vmatrix} \]

Hint:

For a \(2 \times 2\) determinant, simply multiply the diagonal elements and subtract the product of the off-diagonal elements: \(ad - bc\).

Answer 1

Step 1: Recall the formula for a 2×2 determinant.
For a determinant of order 2, \[ \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc \] Step 2: Substitute the given values.
Here, \(a = 4\), \(b = 3\), \(c = 2\), and \(d = 7\). \[ \begin{vmatrix} 4 & 3 \\ 2 & 7 \end{vmatrix} = (4)(7) - (3)(2) \] Step 3: Simplify.
\[ = 28 - 6 = 22 \] Step 4: Conclusion.
Hence, the value of the given determinant is 22.
Final Answer: \[ \boxed{22} \]