Consider the linear operator A4 that rotates the vectors about z-axis by angle and then rescales...

     

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Consider the linear operator A4 that rotates the vectors about z-axis by angle and then rescales the x-, y- and z-components of the resulting vector by factors a, , and y, respectively. a) Derive the matrix representation of such a linear operator by acting with A4 on each of the basis vectors i, j, k. b) Find the vector that is obtained by applying linear operator A to vector a = 2 - 4 + 5k Consider the linear operator A4 that rotates the vectors about z-axis by angle and then rescales the x-, y- and z-components of the resulting vector by factors a, , and y, respectively. a) Derive the matrix representation of such a linear operator by acting with A4 on each of the basis vectors i, j, k. b) Find the vector that is obtained by applying linear operator A to vector a = 2 - 4 + 5k