Question

The eigen values of the matrix \(\begin{bmatrix}4 & 3 \\3 & 4 \end{bmatrix} \) are

• A. 1
• B. 2
• C. 7
• D. 4

Answer 1

The Correct Option is A, C

Step 1: Define the characteristic equation. The characteristic equation is derived from the determinant of \( A - \lambda I \), leading to \( \lambda^2 - 8\lambda + 7 = 0 \). 

Step 2: Calculate the determinant and simplify. The determinant simplifies to \( \lambda^2 - 8\lambda + 7 \), which factors to find the eigenvalues. 

Step 3: Solve for \( \lambda \). Using the quadratic formula, we find the solutions to be \( \lambda = 7 \) and \( \lambda = 1 \), confirming the eigenvalues of the matrix.