the matrix has eigenvalues 0, 2, and 4.
(2 0 2
0 2 0
2 0 2)
determine corresponding eigenvectors.

The eigenvectors of the matrix are , and .

Step-by-step explanation:

The given matrix is

It is given that the matrix has eigenvalues 0, 2, and 4.

For

Using Row operations we get

Let z=1,

At eigen vector is .

Similarly,

For

Using row operations.

At eigen vector is .

For

Using row operations.

at z=1

At eigen vector is .

Therefore the eigenvectors of the matrix are , and .

i dont know sorry

step-by-step explanation:

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .