Question

Problem 1. Choose all in the box that applies to the following set (with explanation): Linearly independent, Orthogonal set, Orthonormal set 4. [1/ 2] [ 1/3] -1/3, 2/6 ( 1/76 (1/3

Answer 1

Solution. 1/3 2/56 (A) 9/7- () V3 let 2IV6 -1/3 +B VE V6 VE from ) in M (뚜-부)» s is linearly indèpendent (by 3)=> B =0 set 1X2 ई orthogonal aso So ser

-1/5 and 21V6 2 + 4x3 + 3X3 A 18 20 2 + 12+6 18 18 + 1. Si is not osthonomal. -'. there { ta()()O} ® let S2 = VT4 2. 92 Nao let VE V5 2) K=B=0 in 4 => V=0 putting Sz is lineartyinderndent

JuE (1+3+ 2) + o not orthogonal.set. not orthogonal lo Set $2 is not orthonormal. $z is limendy inderendemt but epither orthayond hor anthonormal. © let Vis vīg БL b2 Now let B+ Vīg v26 Vis -2. 4. B + ig=0 N২6 ) x 4+ (9) =) foem O & x=0 8 V=o putting & =0, Y=0 inA B = 0.

<a,, as>= Tuz (+3+ 2) #o mot orthogenal.set. Set $2 is not orthononmal Orthoganal lo =) not 8z is linondy inderendent but pogither ortheyond hor asthonormal. So the fs is linegnty independent: given set alho <bzib3 >. < bi, bg> < b, , b) =0> = S2 is oxthogonal so. set Nor < bu bi> = I, <bz be> = 1, < bs, by > =1 So given set is orthogonal as well as athonormal