(1 point) Supppose A is an invertible n×n matrix and v⃗ is an eigenvector of A with associated eigenvalue 8. Convince yourself that v⃗ is an eigenvector of the following matrices, and find the associated eigenvalues. The matrix A4 has an eigenvalue . The matrix A−1 has an eigenvalue . The matrix A+4In has an eigenvalue . The matrix 5A has an eigenvalue .

By definition, if is an eigenvector of (with associated eigenvalue 8), then

Rinse and repeat to find

so that has a corresponding eigenvalue of 4096.

For this to hold, we require , or . So has a corresonding eigenvalue of 1/8.

so that has an associated eigenvalue of 12.

so the eigenvalue of is 40.

it is contrapositive

i could not see the question too well so check yourself again too . this is because i want you to get it correct.

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )