Answer the following questions with justifications. a An analysis led to a matrix A = 10...

 

Transcribed Image Text:

Answer the following questions with justifications. a An analysis led to a matrix A = 10 01 P PP 1 i) Find the conditions on p such that (x, y) A = x Ay is an innerproduct defined on R. [3 marks] ii) Is x = [1,0,0] perpendicular to y = [0,1,0] with respect to the inner product defined in (i)? Find all z perpendicular to both x and y with respect to the inner product defined in (i). [3 marks] b A data scientist had arrived at a model f(x) = [xQx, bTx] where Q is a 3 x 3 symmetric positive definite matrix and x, b R. [1 mark] i) Find the gradient Vxf. ii) To simplify the computation, help him find the linear approximation off about (0,0,0). [2 marks] c The Manager asked the data analyst to find a 2 x 2 matrix M with trace(M)=0 such that (||M-A||2)2 is minimum where A Help the data analyst in finding M. = Co 02 Answer the following questions with justifications. a An analysis led to a matrix A = 10 01 P PP 1 i) Find the conditions on p such that (x, y) A = x Ay is an innerproduct defined on R. [3 marks] ii) Is x = [1,0,0] perpendicular to y = [0,1,0] with respect to the inner product defined in (i)? Find all z perpendicular to both x and y with respect to the inner product defined in (i). [3 marks] b A data scientist had arrived at a model f(x) = [xQx, bTx] where Q is a 3 x 3 symmetric positive definite matrix and x, b R. [1 mark] i) Find the gradient Vxf. ii) To simplify the computation, help him find the linear approximation off about (0,0,0). [2 marks] c The Manager asked the data analyst to find a 2 x 2 matrix M with trace(M)=0 such that (||M-A||2)2 is minimum where A Help the data analyst in finding M. = Co 02