a) Let S be the reflection matrix through span((1,3,1,2), (2,6,4,8), (0,0,2,5)). Find the eigenvalues, eigenspaces, trace,...

  

Transcribed Image Text:

a) Let S be the reflection matrix through span((1,3,1,2), (2,6,4,8), (0,0,2,5)). Find the eigenvalues, eigenspaces, trace, and determinant of the reflection matrix S. [2] b) Suppose B is a 33 matrix and b is a vector in R such that 1 and 3 are two 4 particular solutions of Bx=b. Suppose Row, (B)=(1,c,7). Find the value of c. c) Suppose that A is a 33 real symmetric matrix with the following properties: The eigenvalues 2, 22, , are all different. E = span(u), Espan(v), E = span(w). u=(1,2,1). =(1,1,C) for some constant C. Find the constant C, and find all of the possible vectors that could equal w. a) Let S be the reflection matrix through span((1,3,1,2), (2,6,4,8), (0,0,2,5)). Find the eigenvalues, eigenspaces, trace, and determinant of the reflection matrix S. [2] b) Suppose B is a 33 matrix and b is a vector in R such that 1 and 3 are two 4 particular solutions of Bx=b. Suppose Row, (B)=(1,c,7). Find the value of c. c) Suppose that A is a 33 real symmetric matrix with the following properties: The eigenvalues 2, 22, , are all different. E = span(u), Espan(v), E = span(w). u=(1,2,1). =(1,1,C) for some constant C. Find the constant C, and find all of the possible vectors that could equal w.