Let V and W be subspaces of Rn with V W = {0}. Let S = projV and T = projW. Show that ST

Chapter 4, Problem 19

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QUESTION:

Let V and W be subspaces of  with .  Let  and .  Show that  if and only if V and W are orthogonal subspaces.

 

Questions & Answers

QUESTION:

Let V and W be subspaces of  with .  Let  and .  Show that  if and only if V and W are orthogonal subspaces.

 

ANSWER:

Step 1 of 3

It is given that  and  are the subspaces of  with,

.

Also,

 , .

Then for, ,

Also,

To show that  if and only if  and  are orthogonal subspaces.

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