6.2(7,11,13) 6.3 (6,8,13,10)

6.2(7,11,13) 6.3 (6,8,13,10) - Homework 12 - Solutions 6.2...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Homework 12 - Solutions 6.2 Problem 7 z W if and only if h z, v i = 0 for all v W . Writing v as a linear combination of vectors from , we see that this is equivalent to h z, X j j v j i = 0 This happens if and only if h z, v j i = 0 for all j . 6.2 Problem 11 The ij th etry of AA is the inner product of the j th and i th rows od A . Therefore, AA = I if and only if h v j , v k i = ij whete ij is the Kronecker delta (See page 89). this proves that the rows form and ONB of C n . 6.2 Problem 13 (a) Let x S . Then h x, y i = 0 for all y S , since S S . Therefore, S S . (b) Let x S . For any y S , h x, y i = 0. Therefore, y ( S ) , proving S ( S ) . Since S is a subspace even if S is not, taking the span on both side of the above equation, the proof is complete. (c) By (b), W ( W ) . Suppose x ( W ) . Then, for any z W , h x, z i = 0. On the other hand if x /...
View Full Document

Page1 / 3

6.2(7,11,13) 6.3 (6,8,13,10) - Homework 12 - Solutions 6.2...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online