Show that w is in span(B). B= {-}~-B] We want to solve C₁ 18 2 0498 so set up the augmented matrix of the linear system and row-reduce to solve it: 3

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 31E
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Show that w is in span(B).
We want to solve
B - (-)-~-]
=
W =
-1
Thus C₁ =
048
2 + C₂
so set up the augmented matrix of the linear system and row-reduce to solve it:
[w] B =
12
1
1
0
0 -1
and C₂ =
00
8
[3].
+
Find the coordinate vector [w]B.
3
R₂-2R₁
-=1/R₂2
R₁ - R₂
R₂ + R₂
1 1
0-2
0 -1
1
0 1
0 -1
1
0
0
1
0 0
so that
Transcribed Image Text:Show that w is in span(B). We want to solve B - (-)-~-] = W = -1 Thus C₁ = 048 2 + C₂ so set up the augmented matrix of the linear system and row-reduce to solve it: [w] B = 12 1 1 0 0 -1 and C₂ = 00 8 [3]. + Find the coordinate vector [w]B. 3 R₂-2R₁ -=1/R₂2 R₁ - R₂ R₂ + R₂ 1 1 0-2 0 -1 1 0 1 0 -1 1 0 0 1 0 0 so that
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