Use the Exercise 20 to prove parts (b) and (c) of Theorem 2. A line in the
Question:
A line in the plane has an equation of the form Ax + By + C = 0, where A and B are not both zero. Use the method of Example 8 to show that the image of this line under multiplication by the invertible matrix
has the equation A²x + B²y + C = 0, where
A² = (dA - cB) / (ad - bc) and B² = (-bA + aB) / (ad - bc)
Theorem 2
If T: R2 R2 is multiplication by an invertible matrix, then
(b) The image of a straight line through the origin is a straight line through the origin.
(c) The images of parallel straight lines are parallel straight lines.
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Related Book For
Elementary Linear Algebra with Applications
ISBN: 978-0471669593
9th edition
Authors: Howard Anton, Chris Rorres
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