Prove Theorem 4.7. If A is an n n matrix, then det(kA) = k n det

Question:

Prove Theorem 4.7.

If A is an n × n matrix, then

det(kA) = kⁿ det A

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra A Modern Introduction

ISBN: 978-0538735452

3rd edition

Authors: David Poole

See More Books

Question Posted: Nov 13, 2018 06:07 AM

See More Questions

Prove Theorem 3.9(b). b. If A is an invertible matrix and c is a nonzero scalar, then cA is an invertible matrix and 1 (CA)1 = -A-1
Prove that if A is an n ( n matrix, then det(adj A) = [det(A)]n-1.
Prove: If A is an n x n matrix with complex entries, then det (A)det(A)
Find a harmonic function (x, y) in the right-half plane x > -1 such that on the boundary (-1, y) = 0, y
When a chameleon captures an insect, its tongue can extend 16 cm in 0.10 s. (a) Find the magnitude of the tongue's acceleration, assuming it to be constant. (b) In the first 0.050 s, does the tongue...
The original association rule mining formulation uses the support and confidence measures to prune uninteresting rules. (a) Draw a contingency table for each of the following rules using the...
For each of the following situations, calculate the degrees of freedom $(d f)$, identify the critical values (assume $\mathrm{a}=.05$ [two-tailed]), calculate the standard error of the mean $s$...
A firm produces a perishable food product at a cost of $10 per case. The product sells for $15 per case. For planning purposes, the company is considering possible demands of 100, 200, and 300 cases....
Calculate the solution set of the following system, using Gauss-Jordan elimination method (that is by transforming the augmented matrix of the system in its reduced row echelon form) (a) x+y+z+w= 5...
Comment on the professionalism of the procedures used to make the advertising claim. Why do you believe the researchers performed the data transformations described? A few years ago Vidal Sassoon,...
Using the manufacturer database, construct a frequency distribution for the variable Number of Production Workers. What does the frequency distribution reveal about the number of production workers?
Using the Consumer Food database, construct a histogram for the variable Annual Food Spending. How is the histogram shaped? Is it high in the middle or high near one or both ends of the data? Is it...
For many years, the balanced scorecard was seen as more appropriate for implementing strategy than for planning it. Now that the strategy map has been conceived, does this replace the balanced...
Julie Baskoff has sell short 400 shares of Watercraft Industries at 92 on margin. The leverage ratio is 1.66667 and her broker requires a 35% maintenance margin. If price went up 15% dividends is $1...
Julie Baskoff has sell short 300 shares of Watercraft Industries at 92 on margin. The leverage ratio is 1.66667 and her broker requires a 35% maintenance margin. If price went up 15% dividends is...
Assuming the expected return on the FTSE 100 Index is 18% and the return on UK Government Bonds is6%, what is the expected return on a UK asset, which has a beta of 2.5? Use: R=R+B(R-R f B(RM-R)
Consider a 6-month forward contract written on 100Kg of coffee beans. Assume that the spot price is 10 per Kg and that the continuously compounded risk free rate is r 5% per annum. Suppose that...
If a biomaterial used for a femoral stem is bioactive: A) fibrous encapsulation will occur B) bone will grow at the interface with the implant C) tissues around the implant will die D) the material...
The manager of a bank wants to use an M/M/s queueing model to weigh the costs of extra tellers against the cost of having customers wait in line. The arrival rate is 60 customers per hour, and the...
Find the image of x = k = const under w = 1/z. Use formulas similar to those in Example 1. y| y = 0 -21 -2 -1 -1, /1 12 T -1 -1 y= -2 x =0
In an exercise in Chapter 7, we asked you to conduct a z test to ascertain whether the Graded Naming Test (GNT) scores for Canadian participants differed from the GNT norms based on adults in...
Unsavory researchers know that one can cheat with hypothesis testing. That is, they know that a researcher can stack the deck in her or his favor, making it easier to reject the null hypothesis. a....
Identify the critical t values for each of the following tests: a. A single-sample t test examining scores for 26 participants to see if there is any difference compared to the population, using a p...
A rhino is charging at you, so decide to sedate it with a tranquilizer gun angled at 40 as shown above. The tranquilizer gun can reach a horizontal distance of 49 m when angled at 45. (Assume ideal...
What is the definition of motivation and how can the chef foster an environment of motivation in the kitchen? What methods can a chef implement to motivate the kitchen team? What factors contribute...
Article Review Read the article. Link is given below: https://www.projecttimes.com/articles/avoid-the-top-three-real-causes-of-scope-creep.html Post your thoughts on this article, add references if...

Prove Theorem 4.7. If A is an n n matrix, then det(kA) = k n det

Question:

Step by Step Answer:

To prove Theorem 47 we need to show if B kA then det B k n det A We will begin by proving ...View the full answer

Linear Algebra A Modern Introduction

Students also viewed these Mathematics questions