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Linear Transformation

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Submitted By hina1
Words 256
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Question #3

(a)Clearly T has a linear transformation Kernel of T is the set of all vectors | x1 | x2 | | | in R2 such that |

(*) | T ( | x1 | x2 | | | ) = 0R2 |
This yields the equation 1 x1 +1 x2 | 1 x1 +0x2 | | | = | 0 | 0 | | |
The matrix equation above is equivalent to the following homogeneous system of equations 1 x1 | +1 x2 | = | 0 | 1 x1 | +0 x2 | = | 0 |

| | We now transform the coefficient matrix of the homogeneous system above to the reduced row echelon form to determine the solution space. 1 | 1 | 1 | 0 | | can be transformed by a sequence of elementary row operations to the matrix 1 | 0 | 0 | 1 | |
The reduced row echelon form of the augmented matrix is 1 | 0 | 0 | 1 | | which corresponds to the system 1 x1 | | = | 0 | | 1 x2 | = | 0 |
The leading entries in the matrix have been highlighted in yellow. x1 | = | 0 | x2 | = | 0 |
This means the kernel consists only of the zero vector, and consequently has no basis. Comments | * The nullity of T is 0. This is the dimension of the kernel of L. * T is a one-to-one transformation since ker T = {0R2}. * T is not a one-to-one onto ransformation.Question #1 T=R3 _ R3T(x)=A(x) A X 1 2 1 | 1 -1 12 1 1 | | | X | 2 | 1-4 | | | 0 | -31 | | | | | | Question # 2References http://www.calcul.com/http://www.cse.scu.edu/~atkinson/teaching/su08/247/exam1.pdfhttp://matrixcalc.org/en/slu.htmlhttps://www.easycalculation.com/operations-research/learn-gauss-jordan-elimination.php | |

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