Question 1 of 58beginner🔧 ApplyNumerical1 mark

Evaluate the determinants in Exercises 1 and 2.

  1. ∣24−5−1∣\begin{vmatrix} 2 & 4 \\ -5 & -1 \end{vmatrix}
Correct Answer

18

Exercise: EXERCISE 4.1 | Q: 1 | (Page 6)
For More Understanding

Explanation

To evaluate the determinant of a 2x2 matrix, we use the standard expansion method shown in Example 5 of the provided text. The determinant is calculated as the product of the main diagonal elements minus the product of the off-diagonal elements.

Solution Steps

  1. Step 1: Let the determinant be Δ=∣24−5−1∣\Delta = \begin{vmatrix} 2 & 4 \\ -5 & -1 \end{vmatrix}.

  2. Step 2: Expanding the determinant, we calculate (Product of diagonal elements) - (Product of off-diagonal elements).

  3. Step 3: Substituting the values: Δ=(2)(−1)−(4)(−5)\Delta = (2)(-1) - (4)(-5).

  4. Step 4: Simplifying the expression: Δ=−2−(−20)=−2+20=18\Delta = -2 - (-20) = -2 + 20 = 18.

Next