Question

DETAILS LARLINALG8 4.R.062. Find the coordinate matrix of x in R' relative to the basis B'. B' = {(1, -1, 2, 1), (1, 1, -4,3), (1, 2, 0, 3), (1, 2, -2, 0)}, x = (6,5, -8,2) [x]g: = Hill 11

Answer 1

Antminum X = (6,5,-8,2), B'= {(1,-1, 2, 1), (1,1,-4,3), (1, 2, 0,3), ( 1,2, -2, 0) 3 Let (6,5,-8,2)= 20 (1,-1,2, 2) +d2 (1, 1, -4,3)+48 (2,2,0, 3) +24 (1, 2, -2,0) $165,-8, 2) = (2, +42 + de to4, rd,+ d2 +223 +2249 24456-4)_2-2049441+342 +303 23 ) - ) who have -(1) 21+22+23+24 = 6 -2, +2 +243 +244-5 2d2-402 +0.23-2245-8 21 +382 +32 +0.4y= 2 In matrin form? 6 20 1 1 1 1 22 2 2 -8 -1 23 2 1 -4. 3 o -2 2 1 24 3 0 A 2=b (2) 5 1 Consider augmented d matria [A: 6] 1 2 i 1 -4 3 1 2 0 3 سرم به . G 5 1-8 2 1 य R24 R₂ + R2 1 wowe 11 6 3 11 8 2 1 ol Rg & R3-2 R1 L int 6 1 I 16 3 1 1 1 -2 -4 1-20 0 1 2 0 1 CScanned with CamScanner

R4FR4-R 1 6 - [ os 2 - I b R212, 312 R317 112 1 1 1 2 3 3 I 1 -6 -2 -4 -20 2 2 R3€ Rg+3R2 -1'. -4 오 1 1 I o 2 3 3 I 0 0 7 5 13 0 2 2 2 -4 R4 Fry-R2 1 1 1 "G 1 1 0 2 3 3 !! 0 1 3/2 312,02 7 5 13 ♡ 7 5! 13 0 -4 -15 0-1 4-15 RlER1 - R2 1 0-112 112 112 I 01/2-1/2 1/2 o 1 312 11 o 1 312 31211/2 0 0 7 5 13 1 0 o -1 517 11317 -4 -15 6 -1 Ret Ret R3 1 o 0 -1171017 2 0 1 312 312 1112 0 1 517 0 -4 1-15 R2 & R2 - 3 R3 1 0 -117 1107 1 0 317 o 1 517 1317 0 -1 -4 -15 R4 € Ry TR3 1 -117 | 1017 o 0 317 1917 1 517 i 1317 o -23171 -9217 0 CScanned with CamScanner 4-15 o 1317 I 1917 DOO 1 -

R48 - 12/23 -117 110/17 1 O 0 1 317 1917 5171 1317 1 Į 4 0 0 RIER + I R4 ܝܙ 0 1 0 0 1 2 317 '1917 0 0 1 517 i 1317 0 1 6 4 R24 R2-3 R4 1 0 0 0 1 0 O 1 2 11 517 1317 2 4 0 1 0 0 o R3 R3-55 & R4 0 0 0 1 1 2 ! 1 0 1 0 0 1 0 1 0 o 0 1 14 e get so uning this reduced system. Å a = b we 2,=2 22 = d3-1 04-4 so [a]B di 22 24 rm 28 1 5 Am 2 1 - 1 4 CSScanned with CamScanner
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