Question

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Let Pi- P2 the matte orthogonal, show that the column vectors of the matrix form an orthonormal set. (in the matte la not orthogonal, enter NOT ORTHOGONAL) Find Pia PP- Find Pips PP - Find Pas * P1 Find Pil P.- Find Pal pal- Find al Determine whether the counts of the form orthonormal set. {P.P. } forms an orthonerna som PP does not form another

Answer 1

Let Pa سراسر دبا و/یں P2 = w/t who . میرا /درا We knon that if wit da be 92 an b2 vectoos m. R3 the standard innen between d and product by denoted ard defined by d. B - aebatą be + azba Pe. P2 = £ 5. 27/15 + 3 2 5 + 2/3. (-22) + 25 +371 P2. P2= 0 Pp. P3 = 4 3 2 1 + 2/3 (-2/3) + 2 / 3 / 3 + Pt. P3 . P2. P2 = 2/3. 215 +5.(-2) +63) 11 P2 P₂ = Sima Pa P2 = Pr. P3= P2 P30 , so the matrix P 's or thogonal.

we km от that if be vector in V then norm Euclidean space of denoted by defined as 11211 is 11a11 and rand :: Pla V Pr. Py T(*.* ++5) = VI 11P11 1 11 P211 11 V P2 P2 ş: 3 + Ź * +(-3).(-3) i 3 + + 3 + 2/3 ( VP2 11 - 11P311 P3. P3 V +(-3).(-5)+3.5 12 8+ V VI EI :-1) P31) = I

KOOT that set of vectors ܕܕܠܐܐ ܝ ܝ12 ܐ 9 Euclidean space said Be} in to go thonommal if Ø Bi. Bis zo, Top its for i, 5= 1,2,...). - 1 , and 1 Bill Since and Pt. P2 =0) Pr. P3=0, P2 P₂=0 11 Pell - 11P211 = 11 P31=1 by using ® Z P2, P2, P3} forms onthonormal set. ije Ist option connect.