Eigenvalues and Eigenvectors (original) (raw)

Let A be the 2 × 2 matrix with elements a11 = a12 = a21 = +1 and a22 = −1. Then the eigenvalues of the matrix A19 are

Consider the matrix as given below.

[Tex]\begin{bmatrix} 1&2&3\\ 0&4&7\\ 0&0&3\end{bmatrix}[/Tex]

Which one of the following options provides the CORRECT values of the eigenvalues of the matrix?

Consider the following matrix

[Tex]A = \begin{bmatrix} 2 & 3 \\ x & y \end{bmatrix}[/Tex]

If the eigenvalues of A are 4 and 8, then

How many of the following matrices have an eigenvalue 1?

[Tex]\left[\begin{array}{ll}1 & 0 \\ 0 & 0\end{array}\right],\left[\begin{array}{ll}0 & 1 \\ 0 & 0 \end{array}\right],\left[\begin{array}{cc}1 & -1 \\1 & 1 \end{array}\right][/Tex] and [Tex]\left[\begin{array}{cc} -1 & 0 \\1 & -1 \end{array}\right][/Tex]

What are the eigenvalues of the following 2 × 2 matrix?

[Tex]\begin{bmatrix} 2 & -1 \\ -4 & 5 \end{bmatrix}[/Tex]

The larger of the two eigenvalues of the matrix [Tex]\begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix}[/Tex] is ____

Suppose that the eigenvalues of matrix A are 1, 2, 4. The determinant of (A−1)T is _________

The matrix A has (1, 2, 1)T and (1, 1, 0)T as eigenvectors, both with eigenvalue 7, and its trace is 2. The determinant of A is __________ .

Consider a matrix **P(2x2) whose only eigenvectors are the multiples of [Tex]\begin{bmatrix}1 \\ 4 \end{bmatrix}[/Tex]
Consider the following statements.
(I) **P does not have an inverse
(II) **P has a repeated eigenvalue
(III) **P cannot be diagonalized
Which one of the following options is correct?

Consider the following matrix.

[Tex]\begin{pmatrix}0 & 1 & 1 & 1\\ 1 & 0 & 1 & 1 \\1 & 1 & 0 & 1 \\1 & 1 & 1 & 0\end{pmatrix}[/Tex]

The largest eigenvalue of the above matrix is __________.

There are 10 questions to complete.

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