Question

Question 1 [10 points] Suppose T: M2.2-R3 is a linear transformation whose action on a basis for M2,2 is as follows: Give a basis for the kernel of T and the image of T by choosing which of the original vector spaces each is a subset of, and then giving a set of appropriate vectors. Basis of Kernel is a Subset of M22 Number of Matrices: 1 Bier = {0} Basis of Image is a Subset of M2.2 Number of Matrices: 1

Answer 1

T I 7:13+ [] [2.33:18] 740 33-18 T['s B 116)- T[:: 31 [:) T :o)-TL0310 -E

- T - [:) ] TL. 13-T['_93-1/3!1 - 1700? * [) - [?]+[:] = [3] * 1943: 971.35 + b[!]+[:) +d fool

3a +36-307 atbc -9 +20-30 Labe kere *13 ( 3 - 2:] 3 9+36-30 at b-c -a+20-34 L

[ 3 3 -3 01 2013 L -1 O z -30 ri i lo7 R2 R2 - 1 R RB 1 R3 Rzf Ratri 2 atb=0 b+c=3d tri Loob. = b + ca+b)-3d 2 - a+2b = 1 d= a +23 so ca Cath) so Laterang.[O]+ b Li an] Mar - So Basis of kernel is subset out No of matrices=2

Beste voo. {]. Like I bain of keraar For Image 5 3a +36-367 atbc -9 +20-34 d [ 3 3 -3 0 Tla] - [297 L -1 0 2 -3. After Reducing Matrices

Till o at b-C RB I Rzf Roth, Lo 0 .3 Basis of image is subset of - No. of Marices are 2 Maxi Bima Trillon