Question: Prove that a matrix with rational entries has a rational determinant.

Prove that a matrix with rational entries has a rational determinant.

Step by Step Solution

★★★★★

3.42 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To conclude I can say that a matrix with only rat... View full answer

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

Document Format (1 attachment)

Word file Icon

961-M-L-A-L-S (5636).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Prove that a matrix with all integer entries is convergent if and only if it is nilpotent, i.e., Ak = O for some k. Give a nonzero example of such a matrix.

Q:

Prove that a matrix is diagonalizable if and only if its minimal polynomial has only linear factors.

Q:

(a) Show that if Is a 2 à 2 diagonal matrix with α b, then the only matrices that commute (under matrix multiplication) with D are other 2 à 2 diagonal matrices. (b) What...

Q:

Hi i am very confuse in these problem. Help me out Let M be an n x n matrix of integers. Suppose that M is invertible when viewed as a matrix of rational numbers, i.e., that there exists an n x n...

Q:

MAT 150C, Spring 2017 Practice problems for the final exam This practice sheet contains more problems than the actual exam. Problem marked with stars are more complicated than others. 1. The group S3...

Q:

1. Prove that the set of 2 x 2 matrices with entries from Z and determinant equal to 1 is a group under matrix multiplication. 2. Let G = {[aa] R,a+ a Prove that G is a group under matrix...

Q:

T2 with absolute value 1 (namely the eigenvalue 1). Show that if r = is an In eigenvector of A associated with the eigenvalue 1, then _1, * 0. (This result is true even if some eigenvalues of A are...

Q:

Interview questions 1.) Show that A is idempotent. (2) A = -5 2.) Find the inverse of A. (2) A = 13 3.) (2) Sketch the image of the line segment from (3, 1) to (-2, 4) under the translation (x, y) -...

Q:

1) Give one example of a non-zero matrix A with at least 15 rational entries where the number of rows is larger than the number of columns and its row reduced echelon form. You must use your CSU ID...

Q:

1) Give one example of a non-zero matrix A with at least 15 rational entries where the number of rows is larger than the number of columns and its row reduced echelon form. You must use your CSU ID...

Q:

The accompanying table shows samples of data about Canadian prime ministers, popes, and British monarchs. The values are the numbers of years the subjects lived after they were first elected or were...

Q:

Write a Java program to find all pairs of elements in an array of integer values which their sum is equal to a specified number. Your program should ask user to input the array values and the...

Q:

FASB ASC 1 7 - 5 Accounting Policies in the Construction Industry The FASB ASC provides guidance on disclosures specific to the construction industry. Find, cite, and copy the FASB ASC paragraphs...

Q:

What were the three shocks that the U.S. economy experienced during the period of 20072009? Explain how each of these three shocks can be shown in the ISMP model including the Phillips curve.

Q:

Let A and B be n à n matrices and define 2n à 2n matrices S and M by Determine the block form of S-1 and use it to compute the block form of the product S-1MS. AB O

Q:

Let where A11 is a k à k nonsingular matrix. Show that A can be factored into a product where B = A21A11-1 and C = A22 - A21A11-1A12 Ai A12 A2 A2 O C

Q:

Let A, B, L, M, S, T be n à n matrices with A, B, M nonsingular and L, S, T singular. Determine whether it is possible to find matrices X and Y such that If so, show how; if not, explain why....

Q:

A loan with the following terms is being made: Fixed rate, constant monthly payment. Closing date February 9th. Five percent interest rate. Prepaid interest due at closing. $120,000 mortgage loan...

Q:

(20 points) Your company is considering a five-year project to boost your sales. By purchasing a new machine, you expect to increase sales by X units in years 1 through 5. The per unit price is $70,...

Q:

In ZIMS store the manager is interested in determining which items sell well together. The manager assigned you this task and you opted for using Apriori Algorithm for finding the frequent item sets...