coordinates of x s

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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line algebra and its apps edition 5, section 2.9 question 17E part A) can you explain this?

To mark:
The given statement, "If ß = {vi. ...., vp}, is a basis for a
+ Cp Vp; then c1, ..., p are
subspace Hand if x = cjV1 + .
the coordinates of x relative to the basis P'as true or false.
Expert Solution
Answer to Problem 17E
The given statement is false.
Explanation of Solution
Justification of statement as true:
Apply definition coordinate of vector x as shown below.
"Suppose the set p = {b,..., b,} is the basis for a subspace H.
For each x in H, the coordinates of x relative to the basis ß are the
weights c,..., e, such that x = cbị +. .. +c,b,, and the
vector R° is called the coordinate of vector x (relative to f) or the -
coordinate vector of x."
[x]p
Transcribed Image Text:To mark: The given statement, "If ß = {vi. ...., vp}, is a basis for a + Cp Vp; then c1, ..., p are subspace Hand if x = cjV1 + . the coordinates of x relative to the basis P'as true or false. Expert Solution Answer to Problem 17E The given statement is false. Explanation of Solution Justification of statement as true: Apply definition coordinate of vector x as shown below. "Suppose the set p = {b,..., b,} is the basis for a subspace H. For each x in H, the coordinates of x relative to the basis ß are the weights c,..., e, such that x = cbị +. .. +c,b,, and the vector R° is called the coordinate of vector x (relative to f) or the - coordinate vector of x." [x]p
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