Mathematik-Online problems: Problem 40: Matrix Representation of a Linear Map

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	Mathematik-Online problems:
	Problem 40: Matrix Representation of a Linear Map

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Given the vectors

$\displaystyle b_1=(1, -2, -2)^{{\operatorname t}}, \quad b_2=(0, 1, 1)^{{\opera... ...}, \quad c_1=(3, 0)^{{\operatorname t}}, \quad c_2=(1, 1)^{{\operatorname t}}.$

Let $\alpha: \mathbb{R}^3\longrightarrow\mathbb{R}^2$ be the linear map defined by $b_1\longmapsto c_1$ , $b_2\longmapsto c_2$ and $b_3\longmapsto c_1+c_2$ . $E=\{e_1, e_2, e_3\}$ and $\tilde{E}=\{\tilde{e}_1, \tilde{e}_2\}$ are canonical bases of $\mathbb{R}^3$ respectively $\mathbb{R}^2$ . Find the matrix representation of $\alpha$ with respect to the bases

a) $B=\{b_1, b_2, b_3\}$ and $C=\{c_1, c_2\}$ , b) and $\tilde{E}$ ,

c) and , d) and $\tilde{E}$ .

(Authors: Apprich/Höfert)

see also:

Keyword: Map: linear

automatisch erstellt am 29. 7. 2009

a) $B=\{b_1, b_2, b_3\}$ and $C=\{c_1, c_2\}$ ,		b) and $\tilde{E}$ ,
c) and ,		d) and $\tilde{E}$ .