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**Unformatted text preview: **A = 7 0 4 3 0 3-5 0 1 . 8. Consider the system of equations: 2 x 1-4 x 2-2 x 3 = b 1-5 x 1 + x 2 + x 3 = b 2 7 x 1-5 x 2-3 x 3 = b 3 Describe the set of vectors b for which this system does have a solution. 9. Is the map T : R 3 → R 3 deﬁned by T ( x 1 ,x 2 ,x 3 ) = ( x 2 x 3 ,x 1 x 3 ,x 1 x 2 ) a linear transformation? Why or why not? 1 10. Let T : R 3 → R 3 be the linear transformation given by T ( x 1 ,x 2 ,x 3 ) = ( x 1 ,-x 2 ,x 3 ) ﬁnd the standard matrix of T. 11. ( Challenge ) If T is a one to one linear transformation and u , and v are linearly independent, show that T ( u ), and T ( v ) are linearly independent. 2...

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