A First Course in Linear Algebra by Robert A Beezer

By Robert A Beezer

A primary path in Linear Algebra is an advent to the elemental suggestions of linear algebra, besides an creation to the suggestions of formal arithmetic. It starts with structures of equations and matrix algebra earlier than stepping into the idea of summary vector areas, eigenvalues, linear adjustments and matrix representations. It has a variety of labored examples and workouts, besides specified statements of definitions and entire proofs of each theorem, making it perfect for self sufficient research.

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However, much of the power of linear algebra will be the ability to work with “flat” or “straight” objects in higher dimensions, without concerning ourselves with visualizing the situation. While much of our intuition will come from examples in two and three dimensions, we will maintain an algebraic approach to the subject, with the geometry being secondary. Others may wish to switch this emphasis around, and that can lead to a very fruitful and beneficial course, but here and now we are laying our bias bare.

492 494 494 495 496 498 500 502 503 504 505 508 509 510 Section ILT NIAQ Not injective, Archetype Q . . . . IAR Injective, Archetype R . . . . . IAV Injective, Archetype V . . . . . NKAO Nontrivial kernel, Archetype O . . . TKAP Trivial kernel, Archetype P . . . . NIAQR Not injective, Archetype Q, revisited .

401 401 402 405 407 408 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 414 415 416 417 419 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 428 431 434 434 436 438 439 440 440 443 Section DM SS Some submatrices . . . . . . . . D33M Determinant of a 3 × 3 matrix . . . . MC Minors and cofactors . . . . . . . TCSD Two computations, same determinant .

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