Question

Please write the answer to the following problems and upload the answer in one pdf e ster you finish and submit this final (12 points) Lett be a linear transformation as follows: 2 + 1 - 2 + 2 + 2r 2017 - 2 + 1 + 2 Cal. Find standard matrix representation of (h. Find a basis of Col(A). tel. Find a basis of Null(A) d) Is T 1-17 Is Tonto? Please write the answer to uploading problems including this one on the paper and upload the answer in one pdf file after you finish and submit this Find (10 points) Let A - L :) • [1 Hint when you're picking the linearly independent eigenvectors to form the matrix P. you could pick the eigenvectors that have integer entries instead of you can pick sick (). The computation will be targely simplihed t you do so)

Answer 1

T is not 2 ( A !! -2 1 dan d 2 0 2 -2 2 (b) barts for col (A) es 0:1 instone ist, and & Aah column of ref of a are pirot, the corresponding column of form baris of colAll: (6) basis for mul(A) in the -2 2 as the solu? of anos 2 X3 -225 -2 are x3 -245 Az ins ,As, IER 1) 2 0 43 2x5 15 one one (d). As A donot has pirot in column every to As A do not contain pirol-in pobrecen every yoow, Tis not onto,

2 1 0 -1 1 0 0 1 -1 0 2 -1 0 2 [1 0 0 0 0 2 0 R3 R3+R2X(-1) 1 -1 -1 0 -1 0 -2 -2 1 1 1 2 2 -2 —2 1 1 1 2 R3+R3+Rix(-1) 0 1 1 0 R4 R4+R2X(-2) 0 0 0 1 1 0 2 2 0 2 -2 1 2 0 0 0 -102 Ray RG-R -1 0 2 -2 =rref (A)