Maple1231W5T5 - Further Linear Algebra I

Friday, 24 August 2018

1:04 PM

Machine generated alternative text: Suppose that 111 — 609 93 398 -537 -330 -316 985 -50 -962 507 54 -268 -445 788 113 -431 -234 439 -785 -718 -215 14 and 114 -805 -755 20 165 214 716 851 To avoid typing errors; you can copy and past the following sequences to your Maple worksheet to form entries of the vectors 609, 93, 398, -537, -33€, -316, 985 -5€, -431, -8€5, -962, -234, -755, 5€7, 54, -268, -445, 788 439, -785, -718, -215, 14 2e, 165, 214, 716, 851 (a) Find the dot product of and 112_ Enter your answer in the box below. 1058112

 

Machine generated alternative text: (609: ( -431:-234.439: 14) with(LtnearÅ lgebra) DotProhct(u1: u2) 1058112 ul _u2 1058112 u2 ul 1058112

 

Machine generated alternative text: (b) Suppose that A is the matrix whose columns are these four vectors in order, 4 -46 Let v be the vector 16 12 Enter the values of Al, A = (ul 1 114) Hence Av is a linear combination of the form in the boxes below 4 0 -46 b7)T 16 12 (c) Suppose that Av = (bl b2 Enter the value of b6 in the box below b6 = 24358

 

Machine generated alternative text: (ullu21u31u4) (4-46, 16, 12) Transpose( %) 609 93 398 -537 -330 -316 985 -962 507 54 -268 —445 788 -431 -234 439 -785 -718 -215 14 - 805 -755 20 165 214 716 -11820 31820 - 14466 4 -46 16 12 -11820 31820 - 14466 -15212 2088 24358 -21872 -15212 2088 24358 -21872

 

Machine generated alternative text: Suppose that S {111, 113, u4} where 113 — 205 269 264 -157 20 171 164 263 -232 -62 -54 -229 -212 -221 -260 114 -111 146 -281 192 -281 4591 18233 11908 6131 584 To avoid typing errors; you can copy and past the following sequences to your Maple worksheet to form entries of the vectors or an augmented matrix. 2€5, 171, -54, -111, 4591, 269, 264, -157, 20 164, 263, -232, -62 -229, -212, -221, -260 146, -281, 192, -281 18233, 11908, 6131, 584 The vector v is in the span of S written in the form aul + ßu2 + + 5114 Find a possible set of values for a, ß, 7, 5. Enter the values of a, B, 7, 5 asa sequence in the box below

 

Machine generated alternative text: (20* 269: (171: -62) ( -221:-260) ( 111: -281) (4591: 18233: 11908: 6131: 584) : (ullu21u31u4) 205 269 264 -157 20 LinearSolve(Å, v) 171 164 263 -232 -62 -54 -229 -212 -221 -260 -111 146 -281 192 -281 -29 64 28

 

Machine generated alternative text: Suppose that S -159 - 206 x -286 - 293 - 212 P3@) — 294 + 245 P4}, where 2 145 — 224 2 — 212 2 — 58 x — 240 4 - 191 x 4 - 100 x 4 —170 x 110 — 95 x + 195 x +184 x —60m , and -3459 - 7891 + 26850 + 41888 x3 + 17619 4 To avoid typing errors; you can copy and past the following sequences to your Maple worksheet -159, -206, -145, -224, -191 -286, -293, -212, -212, -100 294, 245, -58, -24€, 110, -95, 195, 184, -3459, -7891, 2685€, -17e -60 41888, 17619 The polynomial p is a linear combination of S written in the form apl + ßP2 + 7'P3 + Find a possible set of values for a, ß, 7, 5. Enter the values of a, B, 7, 5 asa sequence in the box below

 

Machine generated alternative text: with(LtnearÅ lgebra) p. ( -224:-191): (-286:-293: : (294224*-58: -240:-170) . 184:-60) (-3459:-7891: 41888: 17619) LinearSolve( (pl Ip21p31p4), p) 11 -70 _ 90 43

 

Machine generated alternative text: Suppose that S — {111 , 112, 113, 114, 115, 116} C R -81 -40 -90 -98 where u2 -54 -60 113 47 -80 81 -60 114 411 54 -67 -58 115 — -40 69 -71 7 and 116 -67 -8 690 255 535 -305 To avoid typing errors, you can copy and past the following sequences to your Maple worksheet -81, -54, 81, ¯ 71 , 69€, -40, -60, -58, 7, 255, -90, 47, 411, -4€, -67, 535, -98 -80 54 69 -8 -3€5 Since the number of vectors in S is greater that the dimension of R the set S Find a possible setof values for Al, A 4, not all zero, such that Enter the valuesof Al, .\2, as a sequence in the box below must be linearly dependent Hint: There are infinitely many solutions for Al, h, some nice values for the parameters. The solution given by Maple will be in terms of parameters. To get one possible set of values, not all zero, choose

 

Machine generated alternative text: restart : with(LtnearÅ lgebra) -98) 69) (-71, (ullu21u31u41u51u6) GaussianElim inatton( S ) -81 o o LinearSolve(S (O, O, O, O)) -54 o o -81 -54 -40 -60 -90 47 -98 -80 81 -100 o o 81 -60 411 54 -67 2018 81 61463 1350 o -67 -58 -40 69 -71 -67 -71 690 535 -305 3407 81 396649 2700 71170967 122926 690 2315 27 91241 180 355854835 122926

 

Machine generated alternative text: The column space of a matrix A, col(A) is the span of the columns of A. The rank of A is the dimension of col(A). Use Maple to find the dimension of the column space of A, where -2290 -5390 -2766 -4822 2776 9852 24444 11688 21408 -12348 -19137 -49723 -23291 -43959 25206 11147 30233 14205 26969 -15226 19440 50848 24192 44928 -25484 To avoid typing errors; you can copy and past the following sequence of entries of A -2290; -5390, -2766, -4822, 2776, 9852, 24444, 11688; 21408, -12348; -19137, -49723, -23291 -43959, 25206, 11147, 30233, 14205; 26969, -15226; 19440, 50848, 24192, 44928, -25484 and edit it appropriately to make a matrix Enter the rank of A in the box below 5 This question accepts numbers or formulae Plot I Help Switch to Equation Editor Preview

 

Machine generated alternative text: restart : with(LtnearÅ lgebra) Dimension(Å ) RowDtm ension(Å ) ColumnDtm enston(Å ) Rank(Å ) ((-22902 -5390:-2766: 11688221408: 19137:-49723: -23291:-43959: 1420* 26969: 44928, -25484)) -2290 -5390 -2766 -4822 2776 9852 24444 11688 21408 - 12348 -19137 -49723 -23291 -43959 25206 11147 30233 14205 26969 - 15226 19440 50848 24192 44928 -25484

 

 

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