MY-ASSIGNMENTEXPERT™可以为您提供lse.ac.uk MA222 Linear algebra线性代数的代写代考和辅导服务！
这是伦敦政经学校线性代数课程的代写成功案例。
MA222课程简介
Teacher responsible
Dr James Ward
Availability
This course is compulsory on the BSc in Data Science. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.
Pre-requisites
Students should ideally have taken the course Mathematical Methods (MA100) or equivalent, entailing intermediate-level knowledge of linear algebra, linear independence, eigenvalues and diagonalisation.
Prerequisites
This course develops ideas first presented in MA100. It consists of the linear algebra part of MA212, covering the following topics: Vector spaces and dimension. Linear transformations, kernel and image. Real inner products. Orthogonal matrices, and the transformations they represent. Complex matrices, diagonalisation, special types of matrix and their properties. Jordan normal form, with applications to the solutions of differential and difference equations. Singular values, and the singular values decomposition. Direct sums, orthogonal projections, least square approximations, Fourier series. Right and left inverses and generalized inverses.
MA222 Linear algebra HELP（EXAM HELP， ONLINE TUTOR）
True or false questions:
Let $A \mathbf{x}=\mathbf{b}$ be a system of $n$ variables and $m$ equations.
(a) If $mn$, then the system is inconsistent.
(c) If the system is consistent and $m=n$, then the system has unique solution.
(d) If the system is consistent and $m<n$, then the system has infinitely many solutions.
(e) If the system has unique solution, then $m=n$.
\begin{prob}
\begin{prob}
True or false questions:
Let $\boldsymbol{v}1, \boldsymbol{v}_2, \ldots, \boldsymbol{v}_k$ be vectors of $\mathbb{R}^n$ (a) If $\boldsymbol{v}_1, \boldsymbol{v}_2, \ldots, \boldsymbol{v}_k$ are linearly dependent, so are the vectors $\boldsymbol{v}_1, \boldsymbol{v}_2, \ldots, \boldsymbol{v}{k-1}$.
(b) If $\boldsymbol{v}1, \boldsymbol{v}_2, \ldots, \boldsymbol{v}_k$ are linearly independent, so are the vectors $\boldsymbol{v}_1, \boldsymbol{v}_2, \ldots, \boldsymbol{v}{k-1}$.
(c) If $k \geq n$, then $\boldsymbol{v}_1, \boldsymbol{v}_2, \ldots, \boldsymbol{v}_k \operatorname{span} \mathbb{R}^n$.
(d) If $k<n$, then $\boldsymbol{v}_1, \boldsymbol{v}_2, \ldots, \boldsymbol{v}_k$ cannot span $\mathbb{R}^n$.
(e) The vectors $\boldsymbol{v}_1, \boldsymbol{v}_2, \boldsymbol{v}_3$ are linearly dependent if and only if the vectors $\boldsymbol{v}_1+\boldsymbol{v}_2+\boldsymbol{v}_3, \boldsymbol{v}_1+\boldsymbol{v}_2, \boldsymbol{v}_1$ are linearly dependent
Let $A=\left[\begin{array}{ccc}1 & 2 & -1 \ 1 & 2 & 2 / 3 \ 0 & 3 / 2 & -1 / 2\end{array}\right]$ and $B=\left[\begin{array}{ccc}6 & -2 & 4 \ 0 & -5 & 3 \ 1 & -1 / 3 & 2 / 3\end{array}\right]$.
(a) Find $\operatorname{det} A$.
(b) Find $\operatorname{det} B$
(c) Which of the following are invertible? Justify your answer.
(i) $A B^T$
(ii) $(A B)^T$
(iii) $\left(A^T\right)^3$
Let $T: \mathbb{R}^n \rightarrow \mathbb{R}^m$ be a linear transformation, and let $\boldsymbol{v}_1, \boldsymbol{v}_2, \ldots, \boldsymbol{v}_k$ be vectors of $\mathbb{R}^n$.
(a) If the vectors $\boldsymbol{v}_1, \boldsymbol{v}_2, \ldots, \boldsymbol{v}_k$ are linearly dependent, so are the image vectors $T\left(\boldsymbol{v}_1\right), T\left(\boldsymbol{v}_2\right), \ldots, T\left(\boldsymbol{v}_k\right)$.
(b) If the vectors $\boldsymbol{v}_1, \boldsymbol{v}_2, \ldots, \boldsymbol{v}_k$ are linearly independent, so are the image vectors $T\left(\boldsymbol{v}_1\right), T\left(\boldsymbol{v}_2\right), \ldots, T\left(\boldsymbol{v}_k\right)$.
(c) If the image vectors $T\left(\boldsymbol{v}_1\right), T\left(\boldsymbol{v}_2\right), \ldots, T\left(\boldsymbol{v}_k\right)$ are linearly dependent, so are the vectors $\boldsymbol{v}_1, \boldsymbol{v}_2, \ldots, \boldsymbol{v}_k$.
(d) If the image vectors $T\left(\boldsymbol{v}_1\right), T\left(\boldsymbol{v}_2\right), \ldots, T\left(\boldsymbol{v}_k\right)$ are linearly independent, so are the vectors $\boldsymbol{v}_1, \boldsymbol{v}_2, \ldots, \boldsymbol{v}_k$.
Consider the following linear system
Determine the values of $h$ such that the system is consistent and find the general solution for those consistent cases.
MY-ASSIGNMENTEXPERT™可以为您提供LSE.AC.UK MA222 LINEAR ALGEBRA线性代数的代写代考和辅导服务！
