# 线性代数 示例

Simplify each element.

Find the determinant.

The eigenvector is equal to the null space of the matrix minus the eigenvalue times the identity matrix where is the null space and is the identity matrix.

Find the eigenvector using the eigenvalue .

Simplify each element.

Find the null space when .

Write as an augmented matrix for .

Multiply each element of by to make the entry at a .

Multiply each element of by to make the entry at a .

Perform the row operation to make the entry at a .

Perform the row operation to make the entry at a .

Use the result matrix to declare the final solution to the system of equations.

Write a solution vector by solving in terms of the free variables in each row.

Write the solution as a linear combination of vectors.

Write as a solution set.

The solution is the set of vectors created from the free variables of the system.

Find the eigenvector using the eigenvalue .

Simplify each element.

Find the null space when .

Write as an augmented matrix for .

Multiply each element of by to make the entry at a .

Multiply each element of by to make the entry at a .

Perform the row operation to make the entry at a .

Perform the row operation to make the entry at a .

Use the result matrix to declare the final solution to the system of equations.

Write a solution vector by solving in terms of the free variables in each row.

Write the solution as a linear combination of vectors.

Write as a solution set.

The solution is the set of vectors created from the free variables of the system.

The eigenspace of is the list of the vector space for each eigenvalue.

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