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State True or False. Briefly justify your answers. (a) ✈ € R² is ♂ if and only if √ · √ = 0. (b) Two vectors and in Rº are orthogonal if and only if ||√ + √|| = || π – V ||. (c) For every subspace W of R", its orthogonal complement W is a subspace of Rn. (TTTI I

State True or False. Briefly justify your answers. (a) ✈ € R² is ♂ if and only if √ · √ = 0. (b) Two vectors and in Rº are orthogonal if and only if ||√ + √|| = || π – V ||. (c) For every subspace W of R", its orthogonal complement W is a subspace of Rn. (TTTI I

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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State True or False. Briefly justify your answers. (a) √ € R¹ is ♂ if and only if ✈ · (b) Two vectors and √ in Rª are orthogonal if and only if || 7 + √ || = || π – V' ||. (c) For every subspace W of R", its orthogonal complement W is a subspace of R”. (d) If W is a subspace of R", then (W¹)¹ = W. (e) If W is a subspace of R", then WW¹ = {0}. (f) For an m × n real matrix A, CS (A) = (NS (AT))± and RS (A) = (NS (A))+. = 0.
Transcribed Image Text:State True or False. Briefly justify your answers. (a) √ € R¹ is ♂ if and only if ✈ · (b) Two vectors and √ in Rª are orthogonal if and only if || 7 + √ || = || π – V' ||. (c) For every subspace W of R", its orthogonal complement W is a subspace of R”. (d) If W is a subspace of R", then (W¹)¹ = W. (e) If W is a subspace of R", then WW¹ = {0}. (f) For an m × n real matrix A, CS (A) = (NS (AT))± and RS (A) = (NS (A))+. = 0.
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