Solutions Algebra

Let T( a , b , c , )=(a+b)( 5 , 4 , )+(b-2c-a)( 2 , -

Question: Let

T(abc)=(a+b)(54)+(b−2c−a)(2−3)+(3a−5c)(−15)T\left( \begin{matrix} a \\ b \\ c \\ \end{matrix} \right)=\left( a+b \right)\left( \begin{matrix} 5 \\ 4 \\ \end{matrix} \right)+\left( b-2c-a \right)\left( \begin{matrix} 2 \\ -3 \\ \end{matrix} \right)+\left( 3a-5c \right)\left( \begin{matrix} -1 \\ 5 \\ \end{matrix} \right)

Find m and n where T:Rn→RmT:{{\mathbb{R}}^{n}}\to {{\mathbb{R}}^{m}}, and the standard matrix of T. Is the linear transformation one-to-one, onto?

Solution:

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