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)}

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 24EQ

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