Question

While solving a system of linear equations \( AX = B \) using Cramer’s rule, if \includegraphics[]{6.png}

• A. \( 9 \)
• B. \( 13 \)
• C. \( 5 \)
• D. \( 25 \)

Hint:

Cramer’s rule is useful for solving systems of equations where determinant calculations help find unknowns.

Answer 1

The Correct Option is C

Step 1: Solve for \( \alpha \) and \( \beta \) Using Cramer’s rule: \[ \alpha = \frac{\Delta_1}{\Delta}, \quad \beta = \frac{\Delta_2}{\Delta} \] Computing determinants, we find: \[ \alpha = 2, \quad \beta = 1 \] Step 2: Compute \( \alpha^2 + \beta^2 \) \[ \alpha^2 + \beta^2 = 2^2 + 1^2 = 4 + 1 = 5 \] Thus, the correct answer is 5.