7.(6) Let A be a square matrix of size 4x4 and if det(A) = -1. Find...
Let A be a square matrix such that det(al – A) = 212 – 6211 + 9210. What is the size of A? Is A invertible? Why or why not? How many eigenspaces does A have?
Let A be a square matrix such that det(AI – A) = 212 – 6211 + 9210 (3 points) What is the size of A? (4 points) Is A invertible? Why or why not? I (3 points) How many eigenspaces does A have?
Math 2890 QZ-6 SP 2018 1) Find the rank of the following matrix. Also find a basis for the row and column spaces. 1 0 3 3 10 0 -1 2 Find a basis of Null(A) where A is the given matrix. Find the rank of A and dimension of Nul(A). Let B be an invertible 4X4 matrix (a matrix with 4 rows and 4 columns). Is the matrix AATB also invertible? Explain.
4 (1) Find a matrix A „such that (A - 41)-1 3 1 (2) Let A be 3x3 matrix with 4 = 4 Find : (a) det(( 3 A)?(2 A)-') (b) det( 2 A-' + 3 adj (A)) (3)Find the values of a that makes the system has (a) unique solution (b) No Solution. 3 A 7 (4)Find the rank of a matrix 17 0 1 2 (5)Suppose that I : R3 → R2 „such that 2 T (e.) =...
11. Prove one of the following: a. Let A and B be square matrices. If det(AB) + 0, explain why B is invertible. b. Suppose A is an nxn matrix and the equation Ax = 0 has a nontrivial solution. Explain why Rank A<n.
(7 marks) Let the distinct eigenvalues of a square matrix A be denoted by 11, ..., lk. Suppose the corresponding algebraic multiplicities are mi, ..., Mk and that A is similar to an upper-triangular matrix. Show that k k tr(A) midi and det(A) = II (4;)mi i=1 i=1
Problem 6. Let P be an n × n permutation matrix with 1's on the anti-diagonal. Find det(P), Hint: How many exchange permutations are needed to implement P? Problem 6. Let P be an n × n permutation matrix with 1's on the anti-diagonal. Find det(P), Hint: How many exchange permutations are needed to implement P?
(12) (7 marks) Let the distinct eigenvalues of a square matrix A be denoted by 11, ..., dk. Suppose the corresponding algebraic multiplicities are m1, ..., mk and that A is similar to an upper-triangular matrix. Show that k tr(A) = midi and det(A) = II (1;)" i=1 i=1
Part 7 of 8 - Question 7 of 8 1.0 Points , find det A. [100 If A = 0 1 2 O 34 ОАО OB. 2 O C. -2 O D. 10 O E. not defined Reset Selection Part 8 of 8 - Question 8 of 8 1.0 Points 2] [100] 5 and C= 0 0 2 . Which of these matrices have determinant zero? 0 30 [171] -1 0 Consider the matrices A= 3 0 3 , B=...
26. Find det(A-21) if A is the matrix defined in Problem 7. 1 1 7. [1]