I needed help with all of these not just one please and thank you.
7. Suppose A is a 7 à 7 matrix with rank(A) = 5, What is the dimension of ker(A Clearly explain your answer 8. Consider the linear transformation T:R- R given by 3y Also, let B and B' be the bases and B' 1],[ 2 | Find the matrix representative for T relative to these bases, [TIE 9. An n x n matrix A is called nilpotent if there is a positive integer k such that Ae 0. Show that a nonzero nilpotent matrix with real number entries is not similar to an n à n nonzero diagonal matrix with real number entries. [Hint: ifs-AS= D where S is invertible and D is a nonzero diagonal matrix, solve this equation for A and raise to power k.] 1 4 56 2 7 5 10. Determine the eigenvalues of A 0 037 0 0 04 6 -1 11. Diagonalize the matrix A
Show transcribed image text7. Suppose A is a 7 à 7 matrix with rank(A) = 5, What is the dimension of ker(A Clearly explain your answer 8. Consider the linear transformation T:R- R given by 3y Also, let B and B' be the bases and B' 1],[ 2 | Find the matrix representative for T relative to these bases, [TIE 9. An n x n matrix A is called nilpotent if there is a positive integer k such that Ae 0. Show that a nonzero nilpotent matrix with real number entries is not similar to an n à n nonzero diagonal matrix with real number entries. [Hint: ifs-AS= D where S is invertible and D is a nonzero diagonal matrix, solve this equation for A and raise to power k.] 1 4 56 2 7 5 10. Determine the eigenvalues of A 0 037 0 0 04 6 -1 11. Diagonalize the matrix A
