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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.
ORTHONORMAL SETS OF VECTORS127 19.1. Background127 19.2. Exercises 128 ... Problem 174 26.4. Answers to the Odd-Numbered Exercise175 ... 183 Index 185. PREFACE This collection of exercises is designed to provide a framework for discussion in a junior level linear algebra class such as the one I have conducted fairly regularly at Portland State ...
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.
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. Problems: Vector Spaces
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
116 Solutions to Problem Sets contributed this key idea: The circle contains a big square matrix filled by 1’s. The rank of that all-ones matrix is only 1. So we only have to count the rows above and below that square! Multiply by 2 to include the columns to the left and right of the square. 0 √ 2 2 N N 1 0 1 1 The picture shows 1− √ 2 2!
Problem (F'03, #9). Consider a 3x3 real symmetric matrix with determinant 6. Assume (1; 2; 3) and (0; 3; ¡2) are eigenvectors with eigenvalues 1 and 2. Give an eigenvector of the form (1; x; y) for some real x; y which is linearly indepen-dent of the two vectors above. What is the eigenvalue of this eigenvector.
