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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)}. (d) The row space has basis {(1,–1,0,5), (1,2,3, 0)} and nullspace has basis {(1,0, 3, 2)}. (e) The row space has basis {(1,0, 2, 3, 5)} and the left nullspace has basis {(-3,1)}.

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)}. (d) The row space has basis {(1,–1,0,5), (1,2,3, 0)} and nullspace has basis {(1,0, 3, 2)}. (e) The row space has basis {(1,0, 2, 3, 5)} and the left nullspace has basis {(-3,1)}.

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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Plz do subparts c, d,e asap..tysm

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)}. (d) The row space has basis {(1,–1,0,5), (1,2,3, 0)} and nullspace has basis {(1,0, 3, 2)}. (e) The row space has basis {(1,0, 2, 3, 5)} and the left nullspace has basis {(-3,1)}.
Transcribed Image Text: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)}. (d) The row space has basis {(1,–1,0,5), (1,2,3, 0)} and nullspace has basis {(1,0, 3, 2)}. (e) The row space has basis {(1,0, 2, 3, 5)} and the left nullspace has basis {(-3,1)}.
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