Show that (u₁, u₂ is an orthogonal basis for R2. Then express x as a linear combination of the u's. 6 *-[-2] U₁ = 8 X U₂ 16 8 and x = OD. If S= S = {₁,..., up} is a basis in RP, then the members of S span RP and hence form an orthogonal set. What calculation shows that {u₁, u₂} is an orthogonal basis for R²? Since the inner product of u₁, and u₂ is 0, the vectors form an orthogonal set. From the theorem above, this proves that the vectors are also a basis for R2 because they are two linearly independent vectors in R2. Express x as a linear combination of the u's. (Simplify your answers. Use integers or fractions for any numbers in the equation.)
Show that (u₁, u₂ is an orthogonal basis for R2. Then express x as a linear combination of the u's. 6 *-[-2] U₁ = 8 X U₂ 16 8 and x = OD. If S= S = {₁,..., up} is a basis in RP, then the members of S span RP and hence form an orthogonal set. What calculation shows that {u₁, u₂} is an orthogonal basis for R²? Since the inner product of u₁, and u₂ is 0, the vectors form an orthogonal set. From the theorem above, this proves that the vectors are also a basis for R2 because they are two linearly independent vectors in R2. Express x as a linear combination of the u's. (Simplify your answers. Use integers or fractions for any numbers in the equation.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Show that (u₁, u₂ is an orthogonal basis for R2. Then express x as a linear combination of the u's.
6
49
-2
U₁ =
X
8
u₂
16
8
and x =
OD. If S=
S = {₁,..., up} is a basis in RP, then the members of S span RP and hence form an orthogonal set.
What calculation shows that {u₁, u₂} is an orthogonal basis for R²?
Since the inner product of u₁ and ₂ is 0, the vectors form an orthogonal set. From the theorem above, this proves that the vectors are also
because they are two linearly independent vectors in R2.
a basis for R2
Express x as a linear combination of the u's.
(Simplify your answers. Use integers or fractions for any numbers in the equation.)
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