Question

roblem 1: Consider the set of all vectors in R1 which are mutually orthogonal to the vectors <3,4,-1,1> and (a) The first thing you need to do is determine the form of all vectors in this space. Hints on how to proceed You need vectors < a,b,c,d> with the property that <a,b,c,d> is orthogonal to <3,4,-1,1>and <a,b,c,d is orthogonal to <1,1,0,2>. There's a vector equation that defines "orthogonal" and this will set up two equations. .That means you have two equations with four unknowns there are infinitely many solutions for a,b,c,d, but you can parameterize. Rref the system, and parameterize so that That means < a,b,c, d > becomes and b are expressed in terms of C and d <Ithing with c's and d's],[thing with c's and d's],c, d > and you have the form of Scanned our space and can proceed as usual with things in this form CS b re that this set is a subspace of R by explicitly verifying the closure axioms. abasis for the subspace, and give the dimension of the subspace F

Answer 1

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