grandes-ecoles 2014 QIA

grandes-ecoles · France · centrale-maths1__pc Matrices Linear Transformation and Endomorphism Properties

Let $A$ be a real square matrix of size $n$ and $b$ an element of $\mathbb{R}^n$. Let $f$ be the map from $\mathbb{R}^n$ to $\mathbb{R}^n$ defined by $$\forall x \in \mathbb{R}^n \quad f(x) = Ax + b$$ Show that $f$ is of class $C^1$ and specify its Jacobian matrix $J_f(x)$ at every point $x$ of $\mathbb{R}^n$.

Let $A$ be a real square matrix of size $n$ and $b$ an element of $\mathbb{R}^n$. Let $f$ be the map from $\mathbb{R}^n$ to $\mathbb{R}^n$ defined by
$$\forall x \in \mathbb{R}^n \quad f(x) = Ax + b$$
Show that $f$ is of class $C^1$ and specify its Jacobian matrix $J_f(x)$ at every point $x$ of $\mathbb{R}^n$.

Paper Questions

QIA QIB1 QIB2 QIC1 QIC2 QIC3 QIIA QIIB1 QIIB2 QIIB3 QIIC1 QIIC2 QIID1 QIID2 QIID3 QIIIA QIIIB1 QIIIB2 QIIIB3 QIIIB4 QIIIC QIVA1 QIVA2 QIVA3 QIVB QIVC