Use the function to find the image of v and the preimage of w. T(V1, V2, v3) = (4v2 - V1, 4v1 + 5v2), v = (2, –1, –4), w = (7, 14) (a) the image of v

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Use the function to find the image of **v** and the preimage of **w**.

\( T(v_1, v_2, v_3) = (4v_2 - v_1, 4v_1 + 5v_2) \), \( \mathbf{v} = (2, -1, -4) \), \( \mathbf{w} = (7, 14) \)

(a) The image of **v**  
[Answer box]

(b) The preimage of **w** (If the vector has an infinite number of solutions, give your answer in terms of the parameter t.)  
[Answer box]
Transcribed Image Text:Use the function to find the image of **v** and the preimage of **w**. \( T(v_1, v_2, v_3) = (4v_2 - v_1, 4v_1 + 5v_2) \), \( \mathbf{v} = (2, -1, -4) \), \( \mathbf{w} = (7, 14) \) (a) The image of **v** [Answer box] (b) The preimage of **w** (If the vector has an infinite number of solutions, give your answer in terms of the parameter t.) [Answer box]
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