Linear AlgebraPlease help me with this as I would really appreciate it. ### Example Exercises on Circles#### A. Use linear algebra techniques to find the center and the radius of the circle \( a(x^2 + y^2) + bx + cy + d = 0 \) through three given points \((1, 0)\), \((-1, 2)\), and \((3, 1)\). Sketch appropriate picture.In this problem, you are to apply linear algebra concepts to determine the properties of a circle that passes through three specific points. Once you have the equation, identify the circle's center and its radius. Don't forget to sketch the circle as well as the points through which it passes for better visualization.#### B. Find all equations of circles \( a(x^2 + y^2) + bx + cy + d = 0 \) through two given points \((-1, 2)\), and \((3, 1)\). Sketch appropriate pictures.In this exercise, you need to find all possible circles that pass through two specific points. Write down the general equations for these circles and then represent them graphically. Sketching will help illustrate the various circles that meet the criteria of passing through the given points.

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Answered: ^. Use linear algebra techniques to…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Linear Algebra

Please help me with this as I would really appreciate it.

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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