Compute ? ? 10? ? using eigenvalues and eigenvectors of the matrix a
a=
1 14 4
-1 6 -2
-2 24 -7
v=
4
-1
-7
a) show that a has three distinct eigenvalues -1, 0, and 1.
b) determine the corresponding eigenspaces.
c) show that the eigenspaces form a basis of ? ? 3.
d) express v as a linear combination of the eigenspaces.
e) write down the corresponding augmented matrix.
f) solve the system using gauss-jordan elimination.
g) compute a10v.