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b) Do the columns of the above matrix form a basis for R16? What about the rows, do the ows of A form a basis for R16? c) What is det(AT)?

b) Do the columns of the above matrix form a basis for R16? What about the rows, do the ows of A form a basis for R16? c) What is det(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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what is the solution with steps for parts a,b,c?

(a) Compute the determinant of the A || following 16 × 16 matrix A: 0 0 [1 0 000 0 0-1 0 0 0 0 0 0 001000 0 0 0 0 0 2 0 0 0 0 0 0 0 0 10 00 1 0 -1 1 0 0 0 0 0 1/200 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 00 00 00 1 -1 1 1 1 0 OHO OLOLL 0 0 1 0 1 1 1 -1 -1 1 1 -3 4 17207HOOL TION NOO 720220-272032117 -720-178ITIO-22O OCH ZOO700-230071 0 1 -1 0 4 0 -1 1 1 0 1 -2 -2 0 -2-1 -4 -2 0 -46 1 0 HOTZOT-2103302-7 1 1230107222601077 -7-7---7-023-2-2 0-1 0 0 0 0 0 0 200 0006 0 0 0 3 000 00 0 0 0 0 1 000 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 000 0 0 2 -4
Transcribed Image Text:(a) Compute the determinant of the A || following 16 × 16 matrix A: 0 0 [1 0 000 0 0-1 0 0 0 0 0 0 001000 0 0 0 0 0 2 0 0 0 0 0 0 0 0 10 00 1 0 -1 1 0 0 0 0 0 1/200 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 00 00 00 1 -1 1 1 1 0 OHO OLOLL 0 0 1 0 1 1 1 -1 -1 1 1 -3 4 17207HOOL TION NOO 720220-272032117 -720-178ITIO-22O OCH ZOO700-230071 0 1 -1 0 4 0 -1 1 1 0 1 -2 -2 0 -2-1 -4 -2 0 -46 1 0 HOTZOT-2103302-7 1 1230107222601077 -7-7---7-023-2-2 0-1 0 0 0 0 0 0 200 0006 0 0 0 3 000 00 0 0 0 0 1 000 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 000 0 0 2 -4
Hint: Don't do cofactor expansion, try blocking the matrix off. (b) Do the columns of the above matrix form a basis for R16? What about the rows, do the rows of A form a basis for R16? (c) What is det(AT)?
Transcribed Image Text:Hint: Don't do cofactor expansion, try blocking the matrix off. (b) Do the columns of the above matrix form a basis for R16? What about the rows, do the rows of A form a basis for R16? (c) What is det(AT)?
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