Let S be a subspace of R. (a) Write a definition for the orthogonal complement of S in R”. (b) Let A = 102 (193). 14 Fin

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Let S Be A Subspace Of R A Write A Definition For The Orthogonal Complement Of S In R B Let A 102 193 14 Fin 1 (68.8 KiB) Viewed 55 times

Let S be a subspace of R. (a) Write a definition for the orthogonal complement of S in R”. (b) Let A = 102 (193). 14 Find a basis for the orthogonal complement of the row space of A. (c) Let A be an arbitrary m × n matrix. Show that the orthogonal complement of the row space of A is the Nullspace of A. (d) Show that if S has dimension k, then the orthogonal complement of S in R" has dimen- sion nk (use part (c)).