1 answer

Suppose T: M22-R3 is a linear transformation whose action on a basis for M2.2 is as...

Question:

Suppose T: M22-R3 is a linear transformation whose action on a basis for M2.2 is as follows: 6 1 -3 -3 0 1 1 1 T T T T -3 -3

Suppose T: M22-R3 is a linear transformation whose action on a basis for M2.2 is as follows: 6 1 -3 -3 0 1 1 1 T T T T -3 -3 0 1 1 2 1 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 M2,2 Number of Matrices: 1 Bker Coo) Basis of Image is a Subset of M2,2 Number of Matrices: 1 Bim (oo

Answers

SA!? we have 1 1-3 -3 -3 -3 6 -6 6 T 0 JA T-6 6 -6 2 Now, we hare. -3 - 3 -3 + 0 3 2 0 0 1 -3 -3 -3 - 3 a 3 = 0 0 3 o 3 6 T O2 [•]-[8:1=[: :)-[::] [:] +2 + - 0 vent! 5 -S - I - 5 Lo IT: O + O1 72T - [i: ] ==||-][• ] + +[:] 13:] 4:10 -2 T 47 Ч 4 2 -2 Now , we have т + b T Lag] = a TFó ;]* to! :]+Ctto] dil O o 0 -IS 1-4) a b al + b -5 t.d 5 -4 -4 a + 5b-4c-4d -a - 5 b +40 +4d a +5b 4c 4d Kernel of I 0 a b I cd o 0 a + 5b-4c- yd -a - 55-5b +40 +48 b d a a b -5 +4 0 :7+1 abl :7+ cd O - 0 1 Basts of keinee شی a subset of M2x2 Numbu of matrice : 3 -5 +4 - 4 0 kefor image of I contider 5 -4 05 -4 -1 -4 4 4 o 4 -4 0 D --- 5 O 0 As can be seen, only columm I has a fivot element. There in

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