Question

Provide a proof where y = 0 is the only solution to Ay = 0; if...

Provide a proof where y = 0 is the only solution to Ay = 0; if and only if the rank of the m × n matrix A equals q, the number of unknowns

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Given that y′ = Ay(1 − y ) has a solution satisfying y(0) = 12 and...
Given that y′ = Ay(1 − y ) has a solution satisfying y(0) = 12 and y(10) = 24, Find A.
Consider the initial value problem, ay''+by'+cy=0, y(0)=d, y'(0)=f where a,b,c,d and f are constants which one...
Consider the initial value problem, ay''+by'+cy=0, y(0)=d, y'(0)=f where a,b,c,d and f are constants which one of the following could be a solution to the initial value problem? Give breif exlpanation to why the correct answer can be a solution, and why the others can not possibly satisfy the equation. a. sin(t)+e^t b. cost+e^tsint c. cost+1 d. e^tcost
3. For each of the following statements, either provide a short proof that it is true...
3. For each of the following statements, either provide a short proof that it is true (or appeal to the definition) or provide a counterexample showing that it is false. (e) Any set containing the zero vector is linearly dependent. (f) Subsets of linearly dependent sets are linearly dependent. (g) Subsets of linearly independent sets are linearly independent. (h) The rank of a matrix is equal to the number of its nonzero columns.
(a) Show that only one solution exists that satisfy y″ – 9y = 0, y(0) =...
(a) Show that only one solution exists that satisfy y″ – 9y = 0, y(0) = 0, y(ln 2) = 0. (b) Show that only one solution exists that satisfy y″ – 9y = 0, y ′(0) = 5, y ′(ln 2) = –3. (c) Does either result satisfy the Existence and Uniqueness Theorem? Why or why not?
q.1.(a) The following system of linear equations has an infinite number of solutions x+y−25 z=3 x−5 ...
q.1.(a) The following system of linear equations has an infinite number of solutions x+y−25 z=3 x−5 y+165 z=0    4 x−14 y+465 z=3 Solve the system and find the solution in the form x(vector)=ta(vector)+b(vector)→, where t is a free parameter. When you write your solution below, however, only write the part a(vector=⎡⎣⎢ax ay az⎤⎦⎥ as a unit column vector with the first coordinate positive. Write the results accurate to the 3rd decimal place. ax = ay = az =
In this task, you will write a proof to analyze the limit of a sequence. ASSUMPTIONS...
In this task, you will write a proof to analyze the limit of a sequence. ASSUMPTIONS Definition: A sequence {an} for n = 1 to ∞ converges to a real number A if and only if for each ε > 0 there is a positive integer N such that for all n ≥ N, |an – A| < ε . Let P be 6. and Let Q be 24. Define your sequence to be an = 4 + 1/(Pn +...
True or False (5). Suppose the matrix A and B are both invertible, then (A +...
True or False (5). Suppose the matrix A and B are both invertible, then (A + B)−1 = A−1 + B−1 . (6). The linear system ATAx = ATb is always consistent for any A ∈ Rm×n, b ∈Rm . (7). For any matrix A ∈Rm×n , it satisfies dim(Nul(A)) = n−rank(A). (8). The two linear systems Ax = 0 and ATAx = 0 have the same solution set. (9). Suppose Q ∈Rn×n is an orthogonal matrix, then the row...
In this task, you will write a proof to analyze the limit of a sequence. ASSUMPTIONS...
In this task, you will write a proof to analyze the limit of a sequence. ASSUMPTIONS Definition: A sequence {an} for n = 1 to ∞ converges to a real number A if and only if for each ε > 0 there is a positive integer N such that for all n ≥ N, |an – A| < ε . Let P be 6. and Let Q be 24. Define your sequence to be an = 4 + 1/(Pn +...
1. Write a proof for all non-zero integers x and y, if there exist integers n...
1. Write a proof for all non-zero integers x and y, if there exist integers n and m such that xn + ym = 1, then gcd(x, y) = 1. 2. Write a proof for all non-zero integers x and y, gcd(x, y) = 1 if and only if gcd(x, y2) = 1.
You’re the grader. To each “Proof”, assign one of the following grades: • A (correct), if...
You’re the grader. To each “Proof”, assign one of the following grades: • A (correct), if the claim and proof are correct, even if the proof is not the simplest, or the proof you would have given. • C (partially correct), if the claim is correct and the proof is largely a correct claim, but contains one or two incorrect statements or justications. • F (failure), if the claim is incorrect, the main idea of the proof is incorrect, or...