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Exercises for Question Type 2: Finding the eigenvectors corresponding to eigenvalues of a 2x2 matrix - IB | RevisionDojo

Question 1

Find the eigenvalues and corresponding eigenvectors of the matrix $A = \begin{pmatrix}5 & 4\\2 & 3\end{pmatrix}$ .

[6]

Question 2

Find the eigenvectors of the matrix $A = \begin{pmatrix}3 & 0\\0 & 2\end{pmatrix}$ corresponding to its eigenvalues.

[5]

Question 3

Find the eigenvectors of the matrix $A = \begin{pmatrix}2 & 1\\-1 & 4\end{pmatrix}$ corresponding to its eigenvalue(s).

[5]

Question 4

Find the eigenvalues and corresponding eigenvectors of the matrix $A = \begin{pmatrix}4 & -1\\2 & 1\end{pmatrix}$ .

[6]

Question 5

Find the eigenvalues and corresponding eigenvectors of the matrix $A = \begin{pmatrix}1 & 2\\2 & 1\end{pmatrix}$ .

[6]

Question 6

Find the eigenvectors of the matrix $A = \begin{pmatrix}5 & 0\\0 & 5\end{pmatrix}$ corresponding to its eigenvalues.

[4]

Question 7

Find the eigenvectors of the matrix $A = \begin{pmatrix}2 & 1\\0 & 2\end{pmatrix}$ corresponding to its eigenvalues.

[4]

Question 8

Find the eigenvalues and corresponding eigenvectors of the matrix $A = \begin{pmatrix}2 & 1\\1 & 2\end{pmatrix}$ .

[6]

Question 9

Find the eigenvalues and corresponding eigenvectors of the matrix $A = \begin{pmatrix}0 & 1\\-2 & 3\end{pmatrix}$ .

[6]

Question 10

Find the eigenvalues and corresponding eigenvectors of the matrix $A = \begin{pmatrix}6 & -2\\1 & 3\end{pmatrix}$ .

[6]

Question 11

Find the eigenvalues and corresponding eigenvectors of the matrix $A = \begin{pmatrix}4 & 2\\1 & 3\end{pmatrix}$ .

[6]

Question 12

Find the eigenvalues and corresponding eigenvectors of the matrix $A = \begin{pmatrix}1 & 3\\2 & 4\end{pmatrix}$ .

[6]

Question Type 2: Finding the eigenvectors corresponding to eigenvalues of a 2x2 matrix Exercises