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Least Squares Solutions - Linear Algebra - Quiz Solution, Exercises of Linear Algebra

Nalanda Open UniversityLinear Algebra

This is the Quiz Solution of Linear Algebra. Mainly include Row Operation, Resulting Matrix, Requirements, Reduced Row Echelon, Reason, Particular Solution etc. Key important points of tags are: Least Squares Solutions, Matrix, True, Augmented Matrices, Corresponding Rrefs, Orthogonal, Projection, Column Space, Vector, Relationship

Typology: Exercises

2012/2013

Uploaded on 02/27/2013

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Math 205B Quiz 08 page 1 12/04/2009 Name. Soggeste sdotim s 15 6°5 —35 —T a ae) a 9 33 5 4 e 1. Let A be the matrix 0 0-2 2 and let b= : . It’s true that b is not in Col(A); you do not need -10 4 0 -20 6 to verify this. 1A. Find all the least squares solutions x of Ax = b. Write down any augmented matrices you use, along with the corresponding rrefs. Le must fa al abo f AAR = =A" bhi gunn 6 (op rtwded 'y ta Ay nent Mal; : 350 -le -70 770 |2lo ~/40 So 28 ~3o8 |-&4 ~ 70 2g 30 -I?2 |-10 770 = -30g8 -~(? [Plo | 430 rh le | =k @ 2-t2 a A 1 +h x,-2%. l ‘s “2 o e u ° ° ps X= me = Cal eae! tXq gC o oO 0 Pl 2 2a bake 2 ° ( 0 oO Op aca er 0 0 1B. Find the (orthogonal) projection of b on the column space of A. (ca this vector b). /; t i: Tha AX fir amyfonry f te aber 2. om Als]: a . 1C. Find the vector m = b— b. -} - Gis 4 3 |e ak 26 4 era |e 8 SG -10 76 1D. What relationship should m have to Col(A)? Fr dod be in (GIA) ~ 1E. Verify your answer to 1D by finding A?m and explain the result. flim = so Pi (ch ms veder n 17) 6 © ere vedy in 4 ) oot ver ff | [ae ek fl alt, ie, me (CIF S890 1F. What is the least squares error (ie, how far is it from b to Col(A))? thal [7] = [(2) +26" ENEMAS = Slovo ihe Her.