# Suppose a 2 × 2 matrix A has an eigenvector (1 2) , with corresponding eigenvalue −4. what is A(-2 -4) ?

##### 2 Answers

# A ( (-2, -4) ) = ( (8,16) ) #

#### Explanation:

If

# A ul v = lamda ul v #

From which we get with

# A ( (1,2) ) = -4 ( (1,2) ) \ \ \ ..... (star)#

A properties of matrices is that

# A ( (-2, -4) ) = (-2)A ( (1, 2) ) #

# " " = (-2)(-4) ( (1,2) ) # using#(star)#

# " " = 8 ( (1,2) ) #

# " " = ( (8,16) ) #

By definition, the eigenvectors (

**Suppose a 2 × 2 matrix A has an eigenvector (1 2) , with corresponding eigenvalue −4. what is A(-2 -4) ?**

This means that:

So with the question **what is A(-2 -4) ?**: