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tyrasimpson4787
29.05.2020 •
Mathematics
Let v⃗ 1=⎡⎣⎢033⎤⎦⎥,v⃗ 2=⎡⎣⎢1−10⎤⎦⎥,v⃗ 3=⎡⎣⎢30−3⎤⎦⎥ be eigenvectors of the matrix A which correspond to the eigenvalues λ1=−1, λ2=0, and λ3=1, respectively, and let x⃗ =⎡⎣⎢−2−40⎤⎦⎥. Express x⃗ as a linear combination of v⃗ 1, v⃗ 2, and v⃗ 3, and find Ax⃗ . x⃗ = -1 v⃗ 1+ 0 v⃗ 2+ 1 v⃗ 3. Ax⃗ = ⎡⎣⎢⎢⎢⎢⎢⎢ ⎤⎦⎥⎥⎥⎥⎥⎥
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Ответ:
- x as a linear combination :
x = -1 v1+ 0 v2+ 1 v3.
- Transpose Ax = (12, -6, -6)
Step-by-step explanation:
Given v1 = (0 3 3),v2 = (1 −1 0), v3 = (3 0 −3) be eigenvectors of the matrix A which correspond to the eigenvalues λ1 = −1, λ2 = 0, and λ3 = 1, respectively, and let x = (−2 −4 0). Express x as a linear combination of v1, v2, and v3, and find Ax .
To write x as a linear combination of v1, v2, and v3
x = -1 v1+ 0 v2+ 1 v3.
To find Ax
Write A = (0 3 3 )
(1 -1 0)
(3 0-3)
Since transpose x = (-2, 4, 0)
Ax = (0 33 )(-2)
(1 -1 0)(4)
(3 0-3)(0)
= (0×-2 + 3×4 + 3×0)
...(1×-2 + -1×4 + 0×0)
.. (3×-2 + 0×4 + -3×0)
As = (12)
(-6)
(-6)
Transpose Ax = (12, -6, -6)
Ответ:
answer:
9OBZIDH9A
Step-by-step explanation:
NFADOZBN ;IZDFNIPBGSEZNT