# The function is not a linear transformation since

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The function is not a linear transformation, since there exist numbers a , b , c , and d such that T ( a ( b , c , d )) = aT ( b , c , d ).
A = . 0 2 0 0 0 3 T ( x ) = A A = 4 16 8 x 2
T ( x ) = A x = b , 4 2 b 1 16 8 b 2 4 R 1 + R 2 R 2 ~ 4 2 b 1 0 0 4 b 1 + b 2 4 b 1 + b 2 0,
2015 3 17 UW Common Math 308 Section 3.1 7. 2/2 points | Previous Answers HoltLinAlg1 3.1.025. Let for the given matrix A . Determine if T is one-to-one and if T is onto. T ( x ) = A A = 1 −4 −3 11 2 −11 T is one-to-one. T is onto. T is both one-to-one and onto. T is neither one-to-one nor onto. n = 3 > m = 2, 1 −4 0 −3 11 0 2 −11 0 ~ 3 R 1 + R 2 R −2 R 1 + R 3 R 1 −4 0 0 −1 0 0 −3 0 ~ −3 R 2 + R 3 R 1 −4 0 0 −1 0 0 0 0 x 2 3 3 T ( x ) = A x = 0
4/9 9. 3/3 points | Previous Answers HoltLinAlg1 3.1.031. Suppose that for the given A . Sketch a graph of the image under T of the unit square in the first quadrant of R 2 .
8. 2/2 points | Previous Answers HoltLinAlg1 3.1.028. Let for the given matrix A . Determine if T is one-to-one and if T is onto. T ( x ) = A A = 1 2 −5 3 7 −6 −2 −4 6 x , 2 3 2 3