MATH 18 Lecture 13: math18_lecture14
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MATH 18 Full Course Notes
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Last time : vector spaces and subspaces . A subspace of v is subset well which is closed under a linear combs . A vector space a set v which is closed under linear combinations . is. A subspace of v is subset well which is closed under a linear combos. Today : linear maps between vector spaces , and associated subspaces . Tv w where and w are vector spaces , is called a linear transformation if it respects linear combinations. This definition generalizes linear transformations to be arbitrary vector the domain and co domain. T :# rm by allowing spaces . T(a( x ) ) al ( x ) . ,xtazx2+a3x3 two polynomials of degree at most and. + a3x3 and at most 3. ( x ) We have to show that a 3 3 and at most 3. ( x ) + bt ( b ( ) ) for all: be r.
