Part 1 Let A be an m x n matrix, and let beR". Show that if u and v € R" are both solutions of Ax=b, then u - v is a solution of Ax = 0. Part 2 Construct a simple numerical example to Part 1 with a 2 by 3 matrix A.
Part 1 Let A be an m x n matrix, and let beR". Show that if u and v € R" are both solutions of Ax=b, then u - v is a solution of Ax = 0. Part 2 Construct a simple numerical example to Part 1 with a 2 by 3 matrix A.
Part 1 Let A be an m x n matrix, and let beR". Show that if u and v € R" are both solutions of Ax=b, then u - v is a solution of Ax = 0. Part 2 Construct a simple numerical example to Part 1 with a 2 by 3 matrix A.
Linear algebra: please solve both parts correctly and handwritten
Transcribed Image Text:Part 1
Let A be an m x n matrix, and let b e R™.
Show that if u and v € R" are both solutions of Ax=b, then u - v is a solution of
Ax = 0.
Part 2
Construct a simple numerical example to Part 1 with a 2 by 3 matrix A.
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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