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Consider the matrix 1 -1 1 -1 1 1 -1 4 1 -1 A = 0 1 1 2 -2 -2 8 -2 (la) Find bases for the column and null spaces of A. (1b) Find bases for the column and null spaces of AT.

Consider the matrix 1 -1 1 -1 1 1 -1 4 1 -1 A = 0 1 1 2 -2 -2 8 -2 (la) Find bases for the column and null spaces of A. (1b) Find bases for the column and null spaces of AT.

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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I need the 1B answer please.

Consider the matrix 1 -1 0 1 -1 1 1 -1 4 1 -1 A = 0 -1 1 2 -2 4 -2 8 -2 (la) Find bases for the column and null spaces of A. (1b) Find bases for the column and null spaces of AT. (lc) Find bases for the column and null spaces of AAT. (Note:Shortcuts are not allowed) (1d) Find bases for the column and null spaces of ATA. (Note:Shortcuts are not allowed) (le) Conjecture the shortcut. Then use it to find bases for the null spaces of (AA")² and (AT A)².
Transcribed Image Text:Consider the matrix 1 -1 0 1 -1 1 1 -1 4 1 -1 A = 0 -1 1 2 -2 4 -2 8 -2 (la) Find bases for the column and null spaces of A. (1b) Find bases for the column and null spaces of AT. (lc) Find bases for the column and null spaces of AAT. (Note:Shortcuts are not allowed) (1d) Find bases for the column and null spaces of ATA. (Note:Shortcuts are not allowed) (le) Conjecture the shortcut. Then use it to find bases for the null spaces of (AA")² and (AT A)².
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