438CHAPTER 4. MAPPINGS AND TRANSFORMATIONS(c)bardblLbardblis the least number satisfying Equation (4.8).5. Find the operator normbardblLbardblfor each linear mapLbelow:(a)L(x,y) = (y,x).(b)L(x,y) = (x+y,x−y).(c)L(x,y) = (x+y√2,x).(d)L:R2→R2is reflection across the diagonalx=y.(e)L:R2→R3defined byL(x,y) = (x,x−y,x+y).(f)L:R3→R3defined byL(x,y,z) = (x,x−y,x+y).4.3Linear Systems of EquationsA system of equations can be viewed as a single equation involving amapping. For example, the system of two equations in three unknownsbraceleftbiggx+2y+5z=52x+y+7z=4(4.9)can be viewed as the vector equation
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