Question:
The eigen values of the matrix \(\begin{bmatrix}4 & 3 \\3 & 4 \end{bmatrix} \) are
The eigen values of the matrix \(\begin{bmatrix}4 & 3 \\3 & 4 \end{bmatrix} \) are
Updated On: Jan 24, 2025
- 1
- 2
- 7
- 4
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The Correct Option is A, C
Solution and Explanation
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.
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