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MTH501 Assignment No 01 Fall 2019 Solution & Discussion Due Date: 19-11-2019

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MTH501 Linear Algebra Assignment 1 Solution Fall 2019


MTH501 (Fall 2019)

Total marks: 20


Due date: November 19, 2019


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If  {a_1} = \left( \begin{array}{l} \,4\\ 0\\ 0 \end{array} \right)\,\,,\begin{array}{ccccccccccccccc} {\,{a_2} = \left( \begin{array}{l} \,\,\,\,6\\ - \,2\\ - \,8 \end{array} \right)} \end{array} and \begin{array}{ccccccccccccccc} {b = \left( \begin{array}{l} - \,2\\ \,\,\,\,5\\ \,\,\,\,7 \end{array} \right)} \end{array}. Determine whether b  can be generated as a linear combination of {a_1} and {a_2} ? Give complete steps of solution.



Show that the transformation L\,\,:\,\,{R^3} \to {R^2}   defined by L(x\,,\,\,y\,,\,\,z) = (3x + z\,,\,y)  is linear by proving

L(\,\vec u\,\, + \,\,\vec v\,) = L(\vec u) + L(\vec v)  and L(\,c\,\vec u\,) = c\,L\,(\vec u)\,,\,\,where\,\,c\,\,is\,\,scalar

MTH501 Assignment # 1 FALL 2019 COMPLETE SOLUTIO

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