MAT 202 Chapter 2 Questions With Complete Solutions

Linear Transformation correct answer: A function T from Rm to Rn is a L.T if there exists an n x m matrix such that T(x)=Ax for all X in vector space Rm The columns of the matrix of a linear transformation correct answer: The matrix of transformation has column vectors T(e1), T(e2), etc. where e's are the standard vectors Linear Transformation(proofs) correct answer: 1) T(kx)=KT(x) 2) T(x +y)=T(x) +T(y) (x and y in Rm (starting Vector space) and K is a scalar ) Distribution Vector/Transition matrix correct answer: All components addd up to one and all components are positive or zero. Matrix is transition matrix if all column vectors are distribution vectors. If A matrix is a transition matrix then AX will be a distribution vector as well. Scaling by Constant (matrix) correct answer: The matrix is (k 0) Defines scaling up/down by k (0 k) orthogonal Projection ( concept and vector formula) correct answer: Finding the component of our vector parallel to a given line. ProjL(x)=(xu)u=(xw/IwI^2)w where w is a vector parallel to line and u is a unit vector parallel to the line.