Question: You are given n X n matrices A,B,C and you wish to check whether AB = C: Show that Pr[ABx = Cx] = 1/2 if

You are given n X n matrices A,B,C and you wish to check whether AB = C:

Show that Pr[ABx = Cx] = 1/2 if AB <> C. Use this fact to design

a randomized algorithm to check whether AB = C. (Your algorithm should be a

Monte-Carlo algorithm, that is, it should always be efficient but may not always

return the correct answer.) Analyze the time complexity of your algorithm and its success probability, that is,

the probability that it returns the correct answer. How can you improve the success

probability?

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

Hi i need help with the problems highlighted and circled in red, its only linear algebra 176 CHAPTER 2 Matrices and Linear Transformations 4. Give the domain and codomain of the matrix transforma- In...

Q:

The following screenshots are of the questions that I need assistance with. Excel File Edit View Insert Format Tools Data Window Help 59% Sun 10:01 AM QE AutoSave . OFF MGMT 650 HW2...

Q:

1. Use matrix algebra to show that if A is invertible and D satisfies AD = I, then D= A". . . . Choose the correct answer below. O A. Add A"to both sides of the equation AD = I to obtain A" + AD = A"...

Q:

This problem is about matrix operation. In class, I presented the Strassen's algorithm for multiplying two square matrices. Now, we consider a special case of multiplying two square matrices: given...

Q:

2.27. The square of a matrix A is its product with itself, AA. (a) Show that five multiplications are sufficient to compute the square of a 2 2 matrix. (b) What is wrong with the following algorithm...

Q:

Hi, I am stuck with these questions that are attached below. Could you please help me to solve them? Thank you so much! AutoSave ( OFF FXCostSp2020POST Q Q v Home Insert Draw Page Layout Formulas...

Q:

Problem #5: Let A and B be n x n matrices. Which of the following statements are always true? (i) If det(A) = det(B) then det(A B) =0. (ii) If A and B are symmetric, then the matrix AB is also...

Q:

HEY CAN YOU HELP ME SOLVE THE FOLLOWING QUESTIONS: 63, 65, 73, 81, 82, 83 5.3 Diagonalization of Matrices 323 57. [_7 3]: ([:] . ): 43 74. Find a 2 x 2 matrix having eigenvalues 7 and -4, with 58. 2...

Q:

Help me solve this on paper : 1. Assume that A and B are n x n matrices and the equation ABT = 0 has a non-trivial solution. What can be said about matrix AB? 2. If A and B are n x n invertible...

Q:

Please use a recursive algo/Strassen's thm Let A -[ai], B- [b.j] be two n x n matrices. Then the product of A and B is also an n x n matrix CAB- where ! Here, the (i,j)-entry of the product AB is...

Q:

A random sample of size n = 80 is selected from a binomial distribution with population proportion p = .25. a. What will be the approximate shape of the sampling distribution of ? b. What will be the...

Q:

What do we mean when we say that investors and creditors are interested in a companys cash flow prospects?

Q:

What is a potential issue with relying solely on NPV for decision - making? Group of answer choices It is only useful for small projects with short time horizons. It overestimates the value of...

Q:

compute the companies degree of operating leverage, find the company's income, and prepare a contribution margin income statement for the next year if sales decrease by 5% Hudson Company reports the...