Problem 1: Give an example of a 6 x 6 matrix A such that it satisfies...
Exercise 30. Let A be a 5 x 5 matrix. Find the Jordan canonical form J under each of the following assumptions (i) A has only eigenvalue namely 4 and dim N(A- 41) = 4. one (ii) dim N(A 21) = 5. (ii dim N(A -I) = 3 and dim N (A 31) 2. (iv) det(A I) = (1 - )2(2 - A)2 (3 - ) and dim N(A - I) dim N(A - 21) 1 (v) A5 0 and...
6. (42 bonus each) Give a specific example (with numbers) of a matrix M satisfying the given conditions, or explain why no such matrix can exist. (Hint: If such a matrix is possible, give an example in rou echelon form.] (a) M is of size 6 x 4 and rank(M) = 3. (b) M is of size 4 x 6 and rank(M)=5.
6. Give an example of a non-constant sequence that satisfies the given conditions or explain why such a sequence does not exist: (1) {an} is bounded above but not convergent. (2) {an} is neither decreasing nor increasing but still converges. (3) {an} is bounded but divergent. (4) {an} is unbounded but convergent. (5) {an} is increasing and converges to 2.
The Cayley-Hamilton Theorem states that a matrix satisfies its characteristic equation. For example, the characteristic equation of the matrix shown below is as follows. --1:: 22 - 61 + 11 = 0 and by the theorem you have 42 - 64 + 1112 = 0 Demonstrate the Cayley-Hamilton Theorem for the matrix A given below. 03 1 A = -1 5 1 0 0 -1 STEP 1: Find and expand the characteristic equation. STEP 2: Compute the required powers of...
Question 1 Sketch the graph of an example of a function f that satisfies all of the given conditions: f (x) = 3, lim,—2- f (x) = o, lim,—2+ f (x) = -~ lime— fis odd Upload Choose a File
Problem #30: [2 marks] Suppose that a matrix A has characteristic polynomial p() = 1 - 31' + 814 - 23. Consider the following statements. (i) i = 2 is an eigenvalue of A. (ii) A is a 4 x 4 matrix. (iii) That same p() is also the characteristic polynomial of A! Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True...
(a) Let A be a real n x m matrix. (i) State what conditions on n and m, if any, are needed such that the matrix AAT exists. Justify your statement. (ii) Assuming that the matrix AA exists, find its size. (iii) Assuming that the matrix AAT exists, prove using index notation that all diagonal elements of AAT are positive or equal to zero. (iv) Let 12 5 -3 A= 3-4 2 Calculate (AAT) -- (show all your working). 2)
Sketch the graph of an example of a function f that satisfies all of the given conditions. lim f(x) = 4, lim f(x) = 2, lim f(x) = 2, f(3) = 3, f(-1) = 1 x-1 x3+ X-3- у 5 у 5 3 3 -6 - 4 -2 LX 6 N 4 -6 - 4 -2 - 1 - 1 O 5 5 4 ON 3 -6 -4 . -2 2 4 6 -6 -4 -2
MathNetJNLP client Problem 4 Give an example of a quadric curve which satisfies the following con- ditions: I. The curve passes through the point(-7,5) . 2. The tangent line to the curve at at (7-5) is the line 3. The curve is not a line (or a pair of intersecting or parallel lines) 5x ty -40
1. Sketch the graph of an example of a functionſ that satisfies all of the following conditions. lim f(x)=0 lim f(x) - 3 lim f(x) = -50 f(-2) = 0 lim f(x) = -1 lim f(x) = 1 lim f(x) = * f(2)= 1 2 3 -2