# linear_transformation

Jun 17th, 2015
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Simpson University
Course: general
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Miss Julie cannot be stated as tragic heroic. She has to bow down before the social forces which were beyond her control. Jean accepted the naturalist views of the society.

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Question #3(a)Clearly T has a linear transformationKernel of T is the set of all vectorsx1x2in R2such that(*)T(x1x2)=0R2This yields the equation1x1+1x21x1+0x2=00The matrix equation above is equivalent to the followinghomogeneous system of equationsWe now transform the coefficient matrix of the homogeneous system above to the reduced row echelon form to determine the solution space.1110can be transformed by asequence of elementary row operationsto the matrix1001The reduced row echelon form of the augmented matrix is1001which corresponds to the system1x1=01x2=0The leading entries in the matrix have been highlighted in yellow.x1=0x2=0This meansthe kernel consists only of the zero vector, and consequently has no basis.CommentsThenullityof T is 0. This is the dimension of the kernel of L.T is aone-to-onetransformation since ker T = {0R2}.T is not a one-to-oneonto ransformation.Question #1 T=R3 _ R3T(x)=A(x) A X12 11-1 12 1 1X 21-4 0-31 Question # 2References http://www.calcul.com/http://www.cse.scu.edu/~atkinson/teaching/su08/247/exam1.pdfhttp://matrixcalc.org/en/slu.htmlhttps://www.easycalculation.com/operations-research/learn-gauss-jordan-elimination.php

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