Math 2568 Practice Final April 16, 2019Problem 1. True or false? Explain your reasoning. If false, find a condition on A which makes ittrue.(1) If the columns of A are linearly independent, then so are the rows.(2) If A is invertible, then so is AT.(3) If Ax = b has a unique solution for some b ∈ Rm, then nullity(A) = 0.(4) If the only eigenvalue of A is 1, then A is diagonalizable.(5) If A maps orthogonal vectors to orthogonal vectors, then A is orthogonal.Problem 2. Short answer. The answers to all questions below are a single digit between 0 and 9.(1) Compute the determinant of.(2) Suppose 1 is an eigenvalue of A. What number is then an eigenvalue of A + I?(3) Suppose A is a 7 × 9 matrix whose rank is 4. What is the dimension of the row space of A?(4) The matrix�λ 1 0 00 λ 0 00 0 λ 00 0 1 λ�has only one eigenvalue. What is its geometric multiplicity?(5) Suppose�1 2 10 1 01 5 k is not invertible. What is k?Problem 3. Find the Jordan normal form of the following matrices:�Problem 4. Find an orthogonal matrix Q such that QT AQ is diagonal forProblem 5. Consider the matrix�(1) Find 3 linearly independent solutions X1(t), X2(t), X3(t) of the differential equation X0(t) =AX(t).(2) Find a particular solution of the form a1X1(t) + a2X2(t) + a3X3(t) when X(0) =.Problem 6. Find bases for the column space, row space, and null space of the matrix.1Problem 7. Let v ∈ R3 and let A be a 3 × 3 matrix. Suppose v, Av, A2v are all nonzero andA3 = 0.(1) Show that B = {v, Av, A1v} is linearly independent. Deduce B is a basis for R3.(2) Calculate [LA]B where LA is the linear map given by LAx = Ax.Problem 8. Suppose A, B are n × n matrices such that AB = In. Show that BA = In.2本团队核心人员组成主要包括BAT一线工程师，精通德英语！我们主要业务范围是代做编程大作业、课程设计等等。我们的方向领域：window编程 数值算法 AI人工智能 金融统计 计量分析 大数据 网络编程 WEB编程 通讯编程 游戏编程多媒体linux 外挂编程 程序API图像处理 嵌入式/单片机 数据库编程 控制台 进程与线程 网络安全 汇编语言 硬件编程 软件设计 工程标准规等。其中代写编程、代写程序、代写留学生程序作业语言或工具包括但不限于以下范围:C/C++/C#代写Java代写IT代写Python代写辅导编程作业Matlab代写Haskell代写Processing代写Linux环境搭建Rust代写Data Structure Assginment 数据结构代写MIPS代写Machine Learning 作业 代写Oracle/SQL/PostgreSQL/Pig 数据库代写/代做/辅导Web开发、网站开发、网站作业ASP.NET网站开发Finance Insurace Statistics统计、回归、迭代Prolog代写Computer Computational method代做因为专业，所以值得信赖。如有需要，请加QQ：99515681 或邮箱：99515681@qq.com 微信：codehelp QQ：99515681 或邮箱：99515681@qq.com 微信：codehelp
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