Letv⃗ 1=⎡⎣⎢012⎤⎦⎥,v⃗ 2=⎡⎣⎢1−20⎤⎦⎥,v⃗ 3=⎡⎣⎢30−1⎤⎦⎥be eigenvectors of the matrix A which correspond to the eigenvalues λ1=−3, λ2=2
, and λ3=3, respectively, and letx⃗ =⎡⎣⎢−433⎤⎦⎥.Express x⃗ as a linear combination of v⃗ 1, v⃗ 2, and v⃗ 3, and find Ax⃗ .x⃗ = -3 v⃗ 1+ 2 v⃗ 2+ 3 v⃗ 3.Ax⃗ = ⎡⎣⎢⎢⎢⎢⎢⎢ ⎤⎦⎥⎥⎥⎥⎥⎥
