Question: Prove: If A is an n x n matrix with complex entries, then det (A)det(A)

Prove: If A is an n x n matrix with complex entries, then

Prove: If A is an n x n matrix with

det (A)det(A)

Step by Step Solution

★★★★★

3.54 Rating (171 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

We know that detA is the sum of all the signed elementary products a ij1 a 2j2 a ... 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

938-M-L-A-E (1542).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

If A is an n x n matrix, then A is called nilpotent if Ak = O for some positive integer k. (a) Prove that every nilpotent matrix is singular. (b) Verify that is nilpotent. (c) If A is nilpotent,...

Q:

Prove that if A is an n n matrix, then A - AT is skew-symmetric.

Q:

Prove that if A is an n ( n matrix, then det(adj A) = [det(A)]n-1.

Q:

There is an alternative criterion for positive definiteness based on subdeterminants of the matrix. The 2x2 version already appears in (3.62). (a) Prove that a 3 x 3 matrix Is positive definite if...

Q:

3. [2 points each] (a) If A is an m X n matrix, What are the possible values of nullity of A? (b) If A is an m X n matrix and let B be the RREF of A. Show by example that 001(A) 7E col(B). 4. [2...

Q:

Question 1 1 pts What is the system of ODEs a; = 3x1 - x2 + cos(t), a2 = 21 + 4x2 + t - e t in matrix form X' = AX + G? ox - (2 7 ) x + (cos( ) Ox' = (3 1 x + 05 () " = (1 37) x + ((0(2. ) O X' cos (...

Q:

Question 1 1 pts What is the system of ODEs a; = 3x1 - x2 + cos(t), a2 = 21 + 4x2 + t - e t in matrix form X' = AX + G? ox - (2 7 ) x + (cos( ) Ox' = (3 1 x + 05 () " = (1 37) x + ((0(2. ) O X' cos (...

Q:

11. Let A be an n X 71 matrix with complex entries. Prove that 1414* = I if and only if the rows of A form an orthonormal basis for C\". Visit goo. gl/iKcC4S for a solution

Q:

4. [2 points each] (a) Let A be an m x n matrix. Prove that A'A is an n x n matrix with rank(A A) = rank(A). (b) Prove that the square matrix A" A is invertible if and only if rank(A) = n

Q:

Determine the values of the parameter s for which the system has a unique solution, and describe the solution. \f\fAn Inverse Formula Let A be an invertible n x n matrix. Then A-I adj A det A17. Show...

Q:

On July 31, 2010, the end of the first month of operations, Hilton Company prepared the following income statement, based on the absorption costing concept: Prepare a variable costing income...

Q:

A water balloon of mass 890 grams is rolled on level ground with an initial velocity of 38 meters per second. As it travels, water leaks from the balloon at a rate of 255 grams per second. Assume air...

Q:

13.35 Give the value of the test statistic t and the p-value or p-value range for this situation: H0: md 5 0, Ha: md 0, d 5 24, sd 5 15, n 5 50.

Q:

Do you think that the nature of the problems the DVCs face requires government-directed as opposed to a privateenterprise-directed development process? Explain why or why not.

Q:

Answer Exercise 1.7.17 for the system x + 4y - 3z = -3. 25x + 97y - 35z = 39. 35x - 22y + 33 z = -15. Exercise 1.7.17 (a) Find the exact solution to the linear system x - 5 y - z = l.1/6x - 5/6y + z...

Q:

Employ 2 digit arithmetic with rounding to compute an approximate solution of the linear system 0.2x + 2y - 3z = 6, 5x + 43y + 27z = 58, 3x + 23.v - 42z = -87. Using the following methods: (a)...

Q:

(a) Let A be an n n matrix. Which is faster to compute, A1 or A-1? Justify your answer. (b) What about A3 versus A-1? (c) How many operations are needed to compute Ak?

Q:

The new equipment will have a cost of $1,800,000, and it will be depreciated on a straight-line basis over a period of six years (years 1-6). The old machine is also being depreciated on a...

Q:

The Beasley Corporation has been experiencing declining earnings but has just announced a 50 percent salary increase for its top executives. A dissident group of stockholders wants to oust the...

Q:

You are given that 1) Event A = going to school 2) Event B = going to sleep 3)P(A) = 0.20, 4) P(B) = 0.30 5) P(A and B) = 0.12. Explain using math why the events may or may not be independent.