UNDERSTANDING ALGEBRA homework help (Page 3949-3951) - with standard addition and scalar multiplication V:= cfw_a0 1 a1x a2x 2 | a0 a1 a2 R Let d dx V V

# UNDERSTANDING ALGEBRA homework help (Page 3949-3951) - with...

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with standard addition and scalar multiplication; V := {a0 · 1 + a1x + a2x 2 | a0, a1, a2 R} Let d dx : V → V be the derivative operator. The following three equations, along with linearity of the derivative operator, allow one to take the derivative of any 2nd degree polynomial: d dx1 = 0, d dxx = 1, d dxx 2 = 2x . In particular d dx(a01 + a1x + a2x 2 ) = a0 d dx1 + a1 d dxx + a2 d dxx 2 = 0 + a1 + 2a2x. Thus, the derivative acting any of the infinitely many second order polynomials is determined by its action for just three inputs. 6.4 Bases (Take 1) The central idea of linear algebra is to exploit the hidden simplicity of linear functions. It ends up there is a lot of freedom in how to do this. That freedom is what makes linear algebra powerful. 115 116 Linear

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