let b={(0,2,-2)(1,0,-2)} be a basis for a subspace of R^3 and let x=(-1,4,-2)  be a vector in the subspace. find the coordinate matrix of x relative to B. use the GRAM-SCHMIT orthonormalization process to transform B into an orthonormal set B'. find the coordinate matrix of x relative to B'.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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let b={(0,2,-2)(1,0,-2)} be a basis for a subspace of R^3 and let x=(-1,4,-2)  be a vector in the subspace. find the coordinate matrix of x relative to B. use the GRAM-SCHMIT orthonormalization process to transform B into an orthonormal set B'. find the coordinate matrix of x relative to B'.

Expert Solution
Step 1

The given basis vector are b1=0,2,-2, b2=1,0,-2.

The given vector is x=-1,4,-2.

(a)

Therefore the vector x=-1,4,-2 can be written as:

-1,4,-2=a0,2,-2+b1,0,-2=b, 2a,-2a-2b

Solving which, yields b=-1, a=2.

Hence the vector x=-1,4,-2 can be written as:

-14-2=0120-2-22-1

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