Consider the following linear transformation of R3: T(x1, X2, X3) =(-2 · x1 – 2 · x2 + x3, 2 . x1 + 2. x2 – x3, 6 · x1 + 6 - x2 - 3. x3). (A) Which of the following is a basis for the kernel of T? O(No answer given) O ((-1, 1, –3)} O (20, 4), (-1, 1,0), (0, 1, 1)} O{(-1,0, -2), (-1, 1,0)} O {(0, 0,0)} (B) Which of the following is a basis for the image ofT? O(No answer given) O {(2, 0, 4), (1, – 1,0)} O {(1,0, 2), (–1, 1, 0), (0, 1, 1)} O {(1,0, 0), (0, 1, 0), (0,0, 1)} O (-1,1,3)}
Consider the following linear transformation of R3: T(x1, X2, X3) =(-2 · x1 – 2 · x2 + x3, 2 . x1 + 2. x2 – x3, 6 · x1 + 6 - x2 - 3. x3). (A) Which of the following is a basis for the kernel of T? O(No answer given) O ((-1, 1, –3)} O (20, 4), (-1, 1,0), (0, 1, 1)} O{(-1,0, -2), (-1, 1,0)} O {(0, 0,0)} (B) Which of the following is a basis for the image ofT? O(No answer given) O {(2, 0, 4), (1, – 1,0)} O {(1,0, 2), (–1, 1, 0), (0, 1, 1)} O {(1,0, 0), (0, 1, 0), (0,0, 1)} O (-1,1,3)}
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the following linear transformation of R3:
T(x1, x2, X3) =(-2 · x1 - 2. x2 + x3, 2 · x1 + 2 x2 - x3,6 x1 +6. x2 -3 x3).
(A) Which of the following is a basis for the kernel of T?
O(No answer given)
O {(-1, 1, –3)}
O (20, 4), (-1, 1,0), (0, 1, 1)}
O ((-1,0, –2), (-1, 1,0)}
O {(0, 0,0)}
(B) Which of the following is a basis for the image of T?
O(No answer given)
O {(2, 0, 4), (1, –1,0)}
O {(1,0, 2), (–1, 1, 0), (0, 1, 1)}
O {(1,0, 0), (0, 1, 0), (0, 0, 1)}
O {(-1, 1, 3)}
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