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-2 2 07 C=015 -235. C has a pivot position in every row. (ii) -C has a pivot position in every column. (iii) For any b in R³, the equation CX = has a solution. (If false, give an example b which makes it have no solution. If true, explain how you know; maybe cite a theorem.) 33 (vi) The columns of C span R³. The equation CX-6 has only the trivial solution = 0. (If false, write the solution set in parametric vector form. If true, explain how you know; maybe cite a theorem.) The columns of C are a linearly independent set of vectors.

-2 2 07 C=015 -235. C has a pivot position in every row. (ii) -C has a pivot position in every column. (iii) For any b in R³, the equation CX = has a solution. (If false, give an example b which makes it have no solution. If true, explain how you know; maybe cite a theorem.) 33 (vi) The columns of C span R³. The equation CX-6 has only the trivial solution = 0. (If false, write the solution set in parametric vector form. If true, explain how you know; maybe cite a theorem.) The columns of C are a linearly independent set of vectors.

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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-2 20 C 0 1 5 -2 3 5 (ii) (iii) For any bin R, the equation CX = 6 has a solution. (If false, give an example b which makes it have no solution. If true, explain how you know; maybe cite a theorem.) (iv) (v) C has a pivot position in every row. C has a pivot position in every column. (vi) The columns of C span R³. -The equation Co has only the trivial solution = 0. (If false, write the solution set in parametric vector form. If true, explain how you know; maybe cite a theorem.) The columns of C are a linearly independent set of vectors.
Transcribed Image Text:-2 20 C 0 1 5 -2 3 5 (ii) (iii) For any bin R, the equation CX = 6 has a solution. (If false, give an example b which makes it have no solution. If true, explain how you know; maybe cite a theorem.) (iv) (v) C has a pivot position in every row. C has a pivot position in every column. (vi) The columns of C span R³. -The equation Co has only the trivial solution = 0. (If false, write the solution set in parametric vector form. If true, explain how you know; maybe cite a theorem.) The columns of C are a linearly independent set of vectors.
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