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3. Find the determinant by using elementary row reductions. 2 -2 -6 0 10 8 -1 8 5 3 -1 -2 3

3. Find the determinant by using elementary row reductions. 2 -2 -6 0 10 8 -1 8 5 3 -1 -2 3

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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1 1 -3 1. Let A = 2 1 1 -1 -4 (a) Find row(A), col(A), and null(A). Find a basis for row(A), col(A), and Nul(A) respectively. Find the rank and nullity of A. Verify the rank theorem. (Hint: row(A) is the row space which is spanned by the rows of A). 1 (b) Determine whether b = 1 is in col(A), whether w = [2 4 -5] 7 is in row(A), and whether v = -1 is in null(A)? 2. Find the coordinate vector of ū = (2, 3) relative to the basis B = {(1,0), (1, 1)} in vector space R?. 3. Find the determinant by using elementary row reductions. 2 -2 -6 0 10 8 -1 8 3 -1 -2 3
Transcribed Image Text:1 1 -3 1. Let A = 2 1 1 -1 -4 (a) Find row(A), col(A), and null(A). Find a basis for row(A), col(A), and Nul(A) respectively. Find the rank and nullity of A. Verify the rank theorem. (Hint: row(A) is the row space which is spanned by the rows of A). 1 (b) Determine whether b = 1 is in col(A), whether w = [2 4 -5] 7 is in row(A), and whether v = -1 is in null(A)? 2. Find the coordinate vector of ū = (2, 3) relative to the basis B = {(1,0), (1, 1)} in vector space R?. 3. Find the determinant by using elementary row reductions. 2 -2 -6 0 10 8 -1 8 3 -1 -2 3
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