2. Construct a matrix with the required property or explain why such construction is impossible. (a) The column space has basis {(1,0, 2), (0, 1, 3)} and the nullspace has basis {(-1,0,1)}. (b) The column space has basis {(2,1, –1)} and the nullspace has basis {(1,3, 2)}. (c) The column space has basis {(1,2, –3)} and the left nullspace has basis {(1,0, –1)}.
2. Construct a matrix with the required property or explain why such construction is impossible. (a) The column space has basis {(1,0, 2), (0, 1, 3)} and the nullspace has basis {(-1,0,1)}. (b) The column space has basis {(2,1, –1)} and the nullspace has basis {(1,3, 2)}. (c) The column space has basis {(1,2, –3)} and the left nullspace has basis {(1,0, –1)}.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.5: Iterative Methods For Computing Eigenvalues
Problem 51EQ
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