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Find Base for ImT and KerT - Mathematics Stack Exchange Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
V = ImT \\oplus \\ KerT - Mathematics Stack Exchange I'm trying to prove the following: $\ \ \ Im L \oplus KerL = V \ \ $ when $\ \ \ L = T^k \ \ \ $ When: $\mathbb T: V \rightarrow V \ $ and $ ImT \oplus KerT =V$ My take on this is below I would like to know if my proof is a proper one? If not can you point me to where it fails? Any comment's and suggestions would be much appreciated
Methods for choosing $u$ and $dv$ when integrating by parts? Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
linear algebra - Proof that columns of an invertible matrix are . . . Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
What does a having pivot in every row tell us? What about a pivot in . . . $\begingroup$ why does having a pivot in every row necessarily mean Ax=b has at least one solution? Even if there weren't pivots in every row, couldn't we still have solutions—for eg, if A = [4 5 6 ; 0 0 0] and b= [5 ; 0] then we have 4*x_1 + 5*x_2 + 6*x_3 = 5, which does give at least one solution (x_2 and x_3 in particular are free variables), but A doesn't have a pivot in every row
Additive functor over a short split exact sequence. Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
How to find a basis for the intersection of two vector spaces in Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
linear algebra - Why a subspace of a vector space is useful . . . I'm in a linear algebra class and am having a hard time wrapping my head around what subspaces of a vector space are useful for (among many other things!) My understanding of a vector space is that,