PYQs Based Test - 02 : Eigenvalues and Eigenvectors

In the matrix equation $[A]\{X\}=\{R\}$,

[A] = 4 & 8 & 4\
4pt]
8 & 16 & -4\
4pt] 4 & -4 & 15 , \ = 2\
4pt]
1\
4pt] 4 , \ = 32\
4pt]
16\
4pt] 64 .

**One of the eigenvalues of the matrix $[A]$ is:**

Let the eigenvalues of a 2 × 2 matrix A be 1, -2 with eigenvectors x₁ and x₂ respectively. Then the eigenvalues and eigenvectors of the matrix A³ would, respectively, be

Let I be a 100-dimensional identity matrix and E be the set of its distinct (no value appears more than once in E) real eigenvalues. The number of elements in E is .

Suppose that the eigenvalues of matrix A are 1, 2, 4. The determinant of (A⁻¹)${}^T$ is______.

For the matrix A = ≤ft[ {*20c 5&3\\ 1&3 } ], ONE of the normalized eigen vectors is given as