Q2) Let 21, 22, 23, 24, as be real numbers. Compute det ((a.) (1 :) (...
Problem 3. Let 21, 22, 23, 41, 42, y3 be some real numbers, and let A= (1 12 13 (41 42 43); Prove (slowly) that dim (ker(A)) > 2 # dim (col(A)) <1 # dim (raw(A)) <1 + X1y2 = 91.22, x1y3 = y123, 22y3 = 42.23. Show that dim(col(A)) = dim(raw(A)) = 3 - dim(ker(A)).
Suppose 21, 22, 23, 24 ~ N(0, 1) where 21, 22, 23, 24 are all independent. Let X1 = zi + z2 42 = 22 + 23 23 = 23 + 24 Notice that Cov(21,13) = 0 so that Xi and X3 are independent. Which of the following is true? Var (21 | 22) = Var (21 | 22, 23) Var (x1 | x2) > Var (21 | 22, 23) Var (21 | x2) < Var (21 | 22, 23)
(1 point) Let A= 1-1 -3 -37 6 23 22 (4 128] (a) Compute det(A) = (b) Use Cramer's rule to solve the following system { 1 - - 312 611 + 237 401 + 12 + + 313 = 22+ = 8) = 5 -1 2
Let ai, 02, 03, 04, 05 be real numbers. 2 7 1 1 Compute det ((a :) (1 :) ( .) (:) (* .)) 1 1 1 Determine all values of x E R such that matrix 4 0 1 3 C 2 25 A= is invertable. 2 0 0 1 4 0 0 0
Let ai, 02, 03, 04, 05 be real numbers. 2 7 1 1 Compute det ((a :) (1 :) ( .) (:) (* .)) 1 1 1 Determine all values of x E R such that matrix 4 0 1 3 C 2 25 A= is invertable. 2 0 0 1 4 0 0 0
Previous 21 22 23 Next Question 21 of 23 (1 point) Apply the power property of logarithms. Assume that the variables represent real numbers. In 2y = Question 22 of 23 (1 point) Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. Assume that the variables represent positive real numbers. log3
Q4 20 Points Let (a.) 21 be a sequence of real numbers and a ER such that .-+ 4. No fles uploaded Q4.1 10 Points State the definition of " a Please select flies a ". Select files Q4.2 5 Points in 2020. Consider the sequence (6.) 1 given by bn = 24 in <2020 and be Using only the definition of convergence of sequences, show b a . Please select file Select file Q4.3 5 Points Let(). be a...
3. (a) Let z1,z2, z3 € C, prove the following identity: (21 - 22)(22 – 23)(23 – £1) = (22 - 23)+23(23 – £1)+23(21 - 22). (b) In AABC, P is a point on the plane II containing A, B and C. Prove that aPA +bPB2 +cPC2 > abc.
Let -1 1 0 A= 1 1 0 0 -1 1 -1 1 1 21 22 = 24 1 b= ta 19 2 3 Then Az = b represents the following system: 21 - 22 +23 = 1 21-23 + 14 = 2 -22 + 23 - 24 = 3. Select one: 0 True O False Check 2 + 2y = 1 After performing two elementary operations starting with the system one obtains the system 3y = a 2 +...
Show that the cross ratios corresponding to 24 permutations of four 20, 21, 22, 23 can have only the following six values: , 1-λ, λ-1, Show that the cross ratios corresponding to 24 permutations of four 20, 21, 22, 23 can have only the following six values: , 1-λ, λ-1,