Question

Find the coordinate matrix of x relative to the orthonormal basis B in Rn. x =...

Find the coordinate matrix of x relative to the orthonormal basis B in Rn.

x =

(20, 5, 25),

B = {(3/5,4/5,0),(-4/5,3/5,0),(0,0,1)}

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Homework Answers

Answer #1

write bais in matrix

and vector b is

.

.

system Ax=b is

augmented matrix is

3/5 -4/5 0 20
4/5 3/5 0 5
0 0 1 25

convert into Reduced Row Eschelon Form...

Divide row1 by 3/5

1 -4/3 0 100/3
4/5 3/5 0 5
0 0 1 25


Add (-4/5 * row1) to row2

1 -4/3 0 100/3
0 5/3 0 -65/3
0 0 1 25


Divide row2 by 5/3

1 -4/3 0 100/3
0 1 0 -13
0 0 1 25


Add (4/3 * row2) to row1

1 0 0 16
0 1 0 -13
0 0 1 25

reduced system is

coordinate vector is


0 0
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