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4). Let T: R4 → Rª be a linear transformation defined by T(x, y, z, w) = (x+z+w, -3x+3y+tz+w, -x+3y+9z+3w, –5x+3y+5z – w), i). Find the standard matrix A of the transformation T. ii). Find the basis for the row space of T consisting entirely of row vectors of T. iii). Find the basis for the column space of T consisting entirely of column vectors of Т.

4). Let T: R4 → Rª be a linear transformation defined by T(x, y, z, w) = (x+z+w, -3x+3y+tz+w, -x+3y+9z+3w, –5x+3y+5z – w), i). Find the standard matrix A of the transformation T. ii). Find the basis for the row space of T consisting entirely of row vectors of T. iii). Find the basis for the column space of T consisting entirely of column vectors of Т.

Advanced Engineering Mathematics
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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4). Let T : R4 → Rª be a linear transformation defined by T(x, y, z, w) = (x+z+w, –3x+3y+tz+w, –x+3y+9z+3w, –5x+3y+5z – w), i). Find the standard matrix A of the transformation T. ii). Find the basis for the row space of T consisting entirely of row vectors of T. iii). Find the basis for the column space of T consisting entirely of column vectors of Т. iv). Find the basis and dimension of null space of T.
Transcribed Image Text:4). Let T : R4 → Rª be a linear transformation defined by T(x, y, z, w) = (x+z+w, –3x+3y+tz+w, –x+3y+9z+3w, –5x+3y+5z – w), i). Find the standard matrix A of the transformation T. ii). Find the basis for the row space of T consisting entirely of row vectors of T. iii). Find the basis for the column space of T consisting entirely of column vectors of Т. iv). Find the basis and dimension of null space of T.
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