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20 Nov 2019
Question 7: The cokernel: The image and kernel of a linear map L : â V are important examples of subspaces of V and U, respectively. Define what it means to be a subspace of a vector space and verify that indeed ker L and imL are subspaces. Now consider the space cokerL - {[v]lv E V and [v] - [Lv|) Verify that cokerL is a vector space. Consider the map L : R2 â R, where L(z, y)-(x, y, 0, 0, 0). Compute dim(cokerL), dim(im L) and dim(ker L), and compare your answers. Try some other simple examples like this one and look for a pattern.
Question 7: The cokernel: The image and kernel of a linear map L : â V are important examples of subspaces of V and U, respectively. Define what it means to be a subspace of a vector space and verify that indeed ker L and imL are subspaces. Now consider the space cokerL - {[v]lv E V and [v] - [Lv|) Verify that cokerL is a vector space. Consider the map L : R2 â R, where L(z, y)-(x, y, 0, 0, 0). Compute dim(cokerL), dim(im L) and dim(ker L), and compare your answers. Try some other simple examples like this one and look for a pattern.
25 Dec 2022
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