Let \( B = \{ \mathbf{b_1}, \mathbf{b_2}, \mathbf{b_3} \} \) be a basis for a vector space \( V \). Find \( T(3\mathbf{b_1} - 5\mathbf{b_2}) \) when \( T \) is a linear transformation from \( V \) to \( V \) whose matrix relative to \( B \) is \([T]_B = \begin{bmatrix} 0 & -8 & 3 \\ 0 & 2 & -7 \\ 7 & -6 & 2 \end{bmatrix}\).\[ T(3\mathbf{b_1} - 5\mathbf{b_2}) = \boxed{ \; } \]

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Answered: 0 -8 3 Let B= {b,, b2, b3} be a basis…

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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0 -8 3 Let B= {b,, b2, b3} be a basis for a vector space V. Find T(3b, - 5b,) when T is a linear transformation from V to V whose matrix relative to B is [T)R =0 2 -7 7 -6 2 ..... T(3b, - 5b2) =