10_07_concept_questions

# 10_07_concept_questi - 5 Find the invertible submatrix(made of the pivot columns and rows of the matrix-1 1 2 2-2-1 2 1 2-1 2-1 2 6 Decompose(3 2 1

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Concept Questions: 10-07-2011 MA2940: Linear Algebra for Engineers 1) If a subspace S is 7-dimensional in R 9 , subspaces orthogonal to S can have what dimen- sions? 2) If S and S are orthogonal complements in space U , does S S = U ? 3) If NS ( A ) has dimension 4 and RS ( A ) = C ( A T ) has dimension 6, do you have enough information to ﬁnd the size of matrix A ? 4) A T y = d is solvable when d is in which of the 4 subspaces? The solution y is unique when which subspace contains only the zero vector?
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Unformatted text preview: 5) Find the invertible submatrix (made of the pivot columns and rows) of the matrix -1 1 2 2-2-1 2 1 2-1 2-1 2 6) Decompose (3 , 2 , 1) T into v r + v n , where v r is in the row space and v n is in the null space of A = 2 1 4-1-2-4 3-12-12 TA: Kyle Wilson...
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## This note was uploaded on 01/02/2012 for the course MATH 2940 at Cornell University (Engineering School).

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