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  1. linear algebra class such as the one I have conducted fairly regularly at Portland State University. There is no assigned text. Students are free to choose their own sources of information.

  2. Solutions to Problem Sets 1. Three Questions at the End of the Preface. Gilbert Strang, Introduction to Linear Algebra, 6th Edition (2023) 1. When can lines of lengths r,s,t form a triangle? They must satisfy the strict triangle inequalities r < s+t s < r +t t < r +s If we allow equality, the triangle will have angles of 0,0 and 180 degrees.

  3. 4 Solutions to Problem Sets 24 A four-dimensional cube has 24 = 16 corners and 2 · 4 = 8 three-dimensional faces and 24 two-dimensionalfaces and 32 edges. 25 Fact: For any three vectors u,v,w in the plane, some combination cu + dv + ew is the zero vector (beyond the obvious c = d = e = 0). So if there is one combination

  4. Problem Sets for Linear Algebra in Twenty Five Lectures. February 7, 2012. Selected problems for students to hand in. Contents. Problems: What is Linear Algebra. Problems: Gaussian Elimination. Problems: Elementary Row Operations. Problems: Solution Sets for Systems of Linear Equations. Problems: Vectors in Space, n-Vectors.

  5. Problem Sets with Solutions. MIT OpenCourseWare is a web based publication of virtually all MIT course content. OCW is open and available to the world and is a permanent MIT activity.

  6. However if [a, b, c] is not a multiple of [1, 1, 1], (that is at least two of a, b, c are distinct), then the left–to–right test shows that [a, b, c] and [1, 1, 1] are linearly independent and hence form a basis for R(A). Conse-quently rank A = 2 in this case. 11. Let S be a subspace of F n with dim S = m.

  7. answer when u,v,w are in the same plane. 23 A four-dimensional cube has 24 = 16 corners and 2 · 4 = 8 three-dimensional faces and 24 two-dimensionalfaces and 32 edges. 24 Fact: For any three vectors u,v,w in the plane, some combination cu + dv + ew is the zero vector (beyond the obvious c = d = e = 0). So if there is one combination

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