Consider vector space V5 over field F with dimension 5. Consider linear mapping A E L(V5). Furthermore, assume that there are two mutually different non-zero vectors x, y E V5 satisfying Ax = Ay = 0. Then necessarily nul(A) = 2 rk(A) < 3 a · x + y E ker A, a E F
Consider vector space V5 over field F with dimension 5. Consider linear mapping A E L(V5). Furthermore, assume that there are two mutually different non-zero vectors x, y E V5 satisfying Ax = Ay = 0. Then necessarily nul(A) = 2 rk(A) < 3 a · x + y E ker A, a E F
Elementary Linear Algebra (MindTap Course List)
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Chapter5: Inner Product Spaces
Section5.1: Length And Dot Product In R^n
Problem 17E: Consider the vector v=(1,3,0,4). Find u such that a u has the same direction as v and one-half of...
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![Consider vector space V5 over field F with dimension 5. Consider linear mapping A E L(V5).
Furthermore, assume that there are two mutually different non-zero vectors x, y E V5 satisfying
Ax = Ay = 0. Then necessarily
nul(A) = 2
rk(A) < 3
a · x + y E ker A, a E F](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0196b690-7db8-4b88-b2a5-4ca1f9b2d0dc%2Fb91cf676-54b1-465c-9e96-1066a9e8c437%2Ffewxd8h_processed.png&w=3840&q=75)
Transcribed Image Text:Consider vector space V5 over field F with dimension 5. Consider linear mapping A E L(V5).
Furthermore, assume that there are two mutually different non-zero vectors x, y E V5 satisfying
Ax = Ay = 0. Then necessarily
nul(A) = 2
rk(A) < 3
a · x + y E ker A, a E F
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