Question: Prove that if A is a n x n matrix and c is a scalar, then det(c A) = cn det A.

Prove that if A is a n x n matrix and c is a scalar, then det(c A) = cn det A.

Step by Step Solution

★★★★★

3.42 Rating (180 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To conclude I can say that multiplying ... 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

952-M-L-A-E (1784).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

(a) Prove that if A and B are symmetric n n matrices, then so is A + B. (b) Prove that if A is a symmetric n n matrix, then so is kA for any scalar k.

Q:

Prove that, if A is a symmetric matrix with eigenvalues 1, 2,..., n, then the singular values of A are |1|, |2|,..., |n|.

Q:

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

Q:

Linear Algebra Final answer only - No Explanation Section 5.5 Orthonormal Sets: Problem 1 (1 point) Find the missing coordinates such that the three vectors form an orthonormal basis for IR" : -0.6...

Q:

,, kindly solve Consider the Linear Regression Model 1. For any X = x, let Y = x8 + U, where B E R*. 2. X is exogenous. 3. The probability model is { f (u; ) is a distribution on R : E, [U] = 0, Var,...

Q:

Can you please help me with number 12 and number 15. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! 5.7 Matrix Exponentials...

Q:

1. (I) Find all values of A for 1which the following determinant 1will equal [1: 21 4 3 341 (2) Evaluate the following determinant. 1Write your answer as a polynomial in :r: : 2. If A has a row...

Q:

duction to Linear Algebra Examples II Problem 1. If p is a nonnegative integer and is a nonzero scalar, use mathematical induction to show that (A)p = pAp, for every square matrix A. Problem 2. For a...

Q:

Can you please help me with number 31. I have provided the math chapter it came from and the answer from the back of the book: Thank you so much and Best wishes! 5.7 Matrix Exponentials and Linear...

Q:

1. Let B = (v1, .... Un), C= {ul,....un}, and D = (w1,..., Win} be three bases for R". (a) Prove the following identity regarding the change of basis matrices: Pc +DPBAC = l'B +D. (b) Consider the...

Q:

a. Explain the difference between pure risk and speculative risk. b. How does diversifiable risk differ from nondiversifiable risk?

Q:

Match List-I with List-II and select the correct answer using the code given the lists. List-I (Type of List-II (Measurement of deficit) budget deficit) A. Revenue Deficit 1. Gap between total...

Q:

OUR TOPIC IS ANNUITY AND EFFECTIVE RATE PLEASE DRAW THE CASH FLOW DIAGRAM FOR EACH QUESTION 1 You have decided that upon retirement you will buy a mansion in Hawaii with cold cash after 1 3 years....

Q:

Which of the following is the definition of program management? a. Managing of related or similar projects in a coordinated way b. The process of computer program management c. Managing a television...

Q:

In Exercises 1 and 2, find A such that the given set is Col A? 1. 2. 2st 3r s r,s, t real 2r -s-t 2b 3d b 3c-3d,c, d real L c+d

Q:

For the matrices in Exercises 1-2, (a) find k such that Nul A is a subspace of Rk, and (b) find k such that Col A is a subspace of Rk. 1. 2. 4266 6399 3122 2027 5105

Q:

With A as in Exercise 17, find a nonzero vector in Nul A and a nonzero vector in Col A?

Q:

1. What is the best description of federal funds? LA. A market that allows for depository institutions to lend and borrow money, short term, to/from other depository institutions at a rate controlled...

Q:

Wayco Industrial Supply has a pre-tax cost of debt of 7.6 percent, a cost of equity 14.3 percent, and a cost of preferred stock of 8.5 percent. The firm has 220,000 shares of common stock outstanding...

Q:

A project that provides annual cash flows of $15,700 for 9 years costs $86,932 today. If the required return is 15 percent, the NPV for the project is $ and you would reject the project. At a...