a. Prove that if A and B are n x n non-singular matrices, then (AB)-1 = B-'A-1.

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Chapter2: Second-order Linear Odes
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Solve Qa & b step by step with detailed explanations

a. Prove that if A and B are n × n non-singular matrices, then
(AB)-1 = B-'A¯1.
b. Show that under the transformation represented by the matrix M, where
(1 2
M = 2 0
3 -2 -7.
3
-2
the whole space is mapped onto the plane x – 2y + z = 0.
Find the image under this transformation of:
The line x = -y =5
The plane x – y +z = 0, giving your answer in Cartesian form.
i.
ii.
Transcribed Image Text:a. Prove that if A and B are n × n non-singular matrices, then (AB)-1 = B-'A¯1. b. Show that under the transformation represented by the matrix M, where (1 2 M = 2 0 3 -2 -7. 3 -2 the whole space is mapped onto the plane x – 2y + z = 0. Find the image under this transformation of: The line x = -y =5 The plane x – y +z = 0, giving your answer in Cartesian form. i. ii.
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