(c) If A is a square matrix and A2 = 0,then A = 0. (d) Let A, B be two square matrices. If (A + B) 2 = A2 + 2AB + B2 , then AB = BA.
(1 point) A square matrix A is idempotent if A2 = A. Let V be the vector space of all 2 x 2 matrices with real entries. Let H be the set of all 2 x 2 idempotent matrices with real entries. Is H a subspace of the vector space V? 1. Does H contain the zero vector of V? choose 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two matrices in...
Let A be a square matrix. Prove that if A2 = A, then I - 2A is the inverse of I - 2A.
Find aa A2 AS 2. 40mm 50mm Find aa A2 AS 2. 40mm 50mm
Find A+ and A+A and AA+ and x+ (shortest length least square solution) for this matrix A UVT (the SVD b: s given below)and these 48 .60 Find A+ and A+A and AA+ and x+ (shortest length least square solution) for this matrix A UVT (the SVD b: s given below)and these 48 .60
Let A = ( a1 0 ... 0 0 a2 ... 0 ... ... ... 0 0 an) be an n * n matrix, where a1, a2, . . . , an are nonzero real numbers. (a) Find the general solution to the system of equations -> -> x' = A * x (b) Solve the initial value problem x1(0) = x2(0) = · · · = xn(0) = k, for some constant k. (c) Solve the initial value problem (x1(0) x2(0)...
5. Let B be the following matrix in reduced row-echelon form: 1 B= 1 -1 0-1 0 0 2 0 0 0 0 0 0 0 0 (a) (3 pts) Let C be a matrix with rref(C) = B. Find a basis of ker(C). (b) (3 pts) Find two matrices A1 and A2 so that rref(A1) = rref(A2) im(A) # im(A2). B, and 1 (c) (5 pts) Find the matrix A with the following properties: rref(A) = B, is an...
3. Let a >0, and for any A E Rnxn, define Aa aA (a) Prove that for any induced matrix norm, K(Ao) (b) Write the formula for det(Aa) in terms of det(A). estimating well/ill-conditioning of matrices. n(A) . Hint: examine IAall and IAal directly. (c) Based on your result from (a) and (b), comment on whether the determinant is useful for 3. Let a >0, and for any A E Rnxn, define Aa aA (a) Prove that for any induced...
Find A+ and A+A and AA+ and x+ (shortest length least square solution) for this matrix A UVT (the SVD b: s given below)and these 48 .60
-10 0] (1 point) Find a non-zero 2 x 2 matrix A such that A2