Suppose the 2 × 2 matrix a has eigenvalues λ1 = 4 and λ2 = 3, with eigenvectors v1 and v2, respectively. if u = 5v1 + v2, then a 2u is equal to

(a) 25v1 + v2
(b) 25v1 + 3v2
(c) 80v1 + 9v2
(d) 100v1 + 3v2
(e) 400v1 + 9v2

Option C

Step-by-step explanation:

Given A is matrix has Eigen values and \lambda_{2}=3 with Eigen vectors respectively.

and  is the eigen vector, substitute this to A so then

Squaring ‘A’ value ‘4’, we get

Given , from this, the above can be written as

Similarly, and is the eigen vector. Then,

Squaring ‘A’ value ‘3’, we get

To find , multiply in both sides of the equation , we get

Substitute the value that found above,

6 on both sides and twelve on the top and the bottom

step-by-step explanation: