# 4/4 points | Previous Answers HoltLinAlg1 43001 Consider...

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Current Score : 21 / 24 Due : Friday, November 14 2014 10:00 PM PST 1. 4/4 points | Previous Answers HoltLinAlg1 4.3.001. Consider the following matrices. (To make your job easier, an equivalent echelon form is given for the matrix.) Find a basis for the column space of A . (If a basis does not exist, enter DNE into any cell.) A = 1 3 4 2 5 0 3 8 4 1 0 20 0 1 8 0 0 0 UW Common Math 308 Section 4.3 (Homework) YIYAO LIU Math 308, section E, Fall 2014 Instructor: Richard Balka WebAssign The due date for this assignment is past. Your work can be viewed below, but no changes can be made. Important! Before you view the answer key, decide whether or not you plan to request an extension. Your Instructor may not grant you an extension if you have viewed the answer key. Automatic extensions are not granted if you have viewed the answer key. Request Extension ~
Find a basis for the row space of A . (If a basis does not exist, enter DNE into any cell.) 1 0 0 1 -20 -8 [1, 0; 0, 1; -20, -8] Find a basis for the null space of A . (If a basis does not exist, enter DNE into any cell.)
Verify that the Rank-Nullity Theorem holds. (Let m be the number of columns in matrix A .)
Solution or Explanation A basis for the column space, determined from the pivot columns 1 and 2, is A basis for the row space is determined from the nonzero rows of the echelon form, We solve to obtain and so our null space basis is