Eigenspace Classifications

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GRE Quantitative Reasoning › Eigenspace Classifications

Questions 1 - 4
1

Find the eigenvalues of the following matrix, if possible.

The eigenvalues do not exist.

Explanation

In order to find the eigenvalues of a matrix, apply the following formula:

is the identity matrix.

Compute the determinant and set it equal to zero.

Solve for lambda by using the quadratic formula.

2

Find the eigenvalues of the following matrix, if possible.

The eigenvalues do not exist.

Explanation

In order to find the eigenvalues of a matrix, apply the following formula:

is the identity matrix.

Compute the determinant and set it equal to zero.

Solve for lambda by using the quadratic formula.

3

Find the eigenvalues of the following matrix, if possible.

The eigenvalues do not exist.

Explanation

In order to find the eigenvalues of a matrix, apply the following formula:

is the identity matrix.

Compute the determinant and set it equal to zero.

Solve for lambda by using the quadratic formula.

4

Find the eigenvalues of the following matrix, if possible.

The eigenvalues do not exist.

Explanation

In order to find the eigenvalues of a matrix, apply the following formula:

is the identity matrix.

Compute the determinant and set it equal to zero.

Solve for lambda by using the quadratic formula.

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