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Engineering Calculus Notes 450

Engineering Calculus Notes 450 - 438 CHAPTER 4 MAPPINGS AND...

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438 CHAPTER 4. MAPPINGS AND TRANSFORMATIONS (c) bardbl L bardbl is the least number satisfying Equation ( 4.8 ). 5. Find the operator norm bardbl L bardbl for each linear map L below: (a) L ( x,y ) = ( y,x ). (b) L ( x,y ) = ( x + y,x y ). (c) L ( x,y ) = ( x + y 2 ,x ). (d) L : R 2 R 2 is reflection across the diagonal x = y . (e) L : R 2 R 3 defined by L ( x,y ) = ( x,x y,x + y ). (f) L : R 3 R 3 defined by L ( x,y,z ) = ( x,x y,x + y ). 4.3 Linear Systems of Equations A system of equations can be viewed as a single equation involving a mapping. For example, the system of two equations in three unknowns braceleftbigg x +2 y +5 z = 5 2 x + y +7 z = 4 (4.9) can be viewed as the vector equation
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