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be a linear transformation that preserves lengths; that
Chapter , Problem 8E(choose chapter or problem)
QUESTION:
Problem 8E
be a linear transformation that preserves lengths; that is,
.
a. Show that T also preserves orthogonality; that is,
b. Show that the standard matrix of T is an orthogonal matrix.
Questions & Answers
QUESTION:
Problem 8E
be a linear transformation that preserves lengths; that is,
.
a. Show that T also preserves orthogonality; that is,
b. Show that the standard matrix of T is an orthogonal matrix.
ANSWER:
Solution 8E
Step 1 of 3
a)
Suppose are two vectors such that
It is stated that the linear transformation, preserves lengths
That is for all in .
The strategy of solution is to show that preserves the orthogonality.
The norm of sum of vectors is,
Since
By the Pythagorean Theorem we have