Find the coordinate matrix of x in R" relative to the basis B'. B' = {(4, 3, 3), (-11, 0, 11), (0, 9, 2)}, x = (26, 3, -19)

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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Find the coordinate matrix of x in R" relative to the basis B'.
B' = {(4, 3, 3), (-11, 0, 11), (0, 9, 2)}, x = (26, 3, –19)
%3D
[x]g =
%3!
Transcribed Image Text:Find the coordinate matrix of x in R" relative to the basis B'. B' = {(4, 3, 3), (-11, 0, 11), (0, 9, 2)}, x = (26, 3, –19) %3D [x]g = %3!
Expert Solution
Step 1

The given vector space is  with basis B'=4,3,3, -11,0,11, 0,9,2.

Consider the vector x=26,3,-19R3.

We have to find the coordinate matrix of x in R3 relative to the basis B'.

Suppose that the coordinate matrix of x in R3 relative to the basis B' be xB'=abc.

Then, we  must have x=a4,3,3+b-11,0,11+c0,9,2.

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