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7. (10pts) Show that {u1, U2, u3}is an orthogonal basis for R°. Then express x as a linear combination of the us. -i]--}-|--

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lit uit Now 4,4g= 2-2=0 47.43= 1-1=0 U9:43 = 2+2-420 Uiu;=o titj qu, 42, 433 ü an ie. orthogonal set.NOW Now 10 -1 4 1 a Also, so, 9 Ala Peti)+1(8+1) = 9+9 = 18 9 0 Glumns of A are linearly independent dim R² 3 : qui, 48, 433suppose xa auit bug+ (43. 15) 1 a +25+0 1 -a +2btc Il l -5+4C the of above system is Augmented matrix lid | !s R2 + Rat Ro II

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