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15. Let A be the matrix -3 -5 1 -3 1 A 3 -1 -3 -9 3 and let T : R³ → Rª be the linear transformation defined by T(x) = Ax. By referring to the Fundamental Theorem of Linear Algebra we know that %3D a. dim(ker(T)) + dim(Range(T)) = b. Find a basis for ker(T) and a basis for Range(T). Based on the work done in part b we find that dim(ker(T)) = and dim(Range(T)) С.

15. Let A be the matrix -3 -5 1 -3 1 A 3 -1 -3 -9 3 and let T : R³ → Rª be the linear transformation defined by T(x) = Ax. By referring to the Fundamental Theorem of Linear Algebra we know that %3D a. dim(ker(T)) + dim(Range(T)) = b. Find a basis for ker(T) and a basis for Range(T). Based on the work done in part b we find that dim(ker(T)) = and dim(Range(T)) С.

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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15. Let A be the matrix -3 -5 1 -3 1 -2 A = 3 5 5 -1 | -3 -9 3 and let T: R3 → R4 be the linear transformation defined by T(x) = Ax. %3D By referring to the Fundamental Theorem of Linear Algebra we know that a. dim(ker(T)) + dim(Range(T)) = b. Find a basis for ker(T) and a basis for Range(T). Based on the work done in part b we find that dim(ker(T)) and dim(Range(T)) = с. %3D %3D
Transcribed Image Text:15. Let A be the matrix -3 -5 1 -3 1 -2 A = 3 5 5 -1 | -3 -9 3 and let T: R3 → R4 be the linear transformation defined by T(x) = Ax. %3D By referring to the Fundamental Theorem of Linear Algebra we know that a. dim(ker(T)) + dim(Range(T)) = b. Find a basis for ker(T) and a basis for Range(T). Based on the work done in part b we find that dim(ker(T)) and dim(Range(T)) = с. %3D %3D
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