Question

Math 287, ME/MQ 01 3. Consider the set W of all 2 x 2 matrices of the form with the standard operations of matrix addition and scalar multiplication (a) Show that this set is closed under the operation of addition, (b) Ifu,EW and c is a real munber, show that cu + v) cu + cv. (c) Display the zero vector for W.

Answer 1

under the operation of matrix addison and scalar multiplication @ To show w is closed we let, a. (,6) EW ,631 813) Ew. Where P., 21, B2, Q are all reel numbers: Now, atb. 10b lopen lạo olo Pitpal 2 10 P3) US as P., PER opitp2= B ER and also for. 94 2 2 4ER at btw.. since a and b are arbitrary so for any a, btw 7 atbfW, Hence w is closed under Seaton the operation of addition. Scanned with Scanner.

6 If ur Ewe and a is a real number Let u=) 10:130) Now, cuto) pe ([26]+[$]) sero parol (auto o 210 c(P+r) ) | C(918) o 10 cpter) (cates o Non cuter acrop q o lor - (028) troen °) "les o) 210 epten lates o Hence, Telutu) cutere

to display the zero rector of from the property of zero rector we have uto au whe u-cople het, o = ( x ) Ew *** (P)+(86)-(?!) => [o prvey 106 Dm 2on both sides, trop 0 .-> Kro ataa 31-0 Hence zero reefer of w is. 0-100) widto necev CamScanner