Let A = [a ij ] be a 3 x 3 matrix. Show that det(A T )

Question:

Let A = [a_ij ] be a 3 x 3 matrix. Show that det(A^T) = det A by expanding det A along its first row and det(A^T) along its first column.

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

Step by Step Answer:

Related Book For book-img-for-question

Differential Equations And Linear Algebra

ISBN: 9780134497181

4th Edition

Authors: C. Edwards, David Penney, David Calvis

See More Books

Question Posted: Jul 06, 2023 06:51 AM

See More Questions

Suppose you are considering investing in a mutual fund that has an expense ratio of 1.5% and has returned 10% annually over the past 5 years. If you plan to invest $10,000 in the fund for the next 10...
Let J be the n ( n matrix of all 1's and consider A = (a - b)I + b J ; that is, Confirm that det A = (a - b)n-1 [a + (n - 1)b] as follows: a. Subtract row 2 from row 1, row 3 from row 2, and so on,...
Let A be a 4 Ã 3 matrix with a2 = a3. If b = a1 + a2 + a3, then the system Ax = b will have infinitely many solutions. In this case answer true if the statement is always true and false...
In a bank reconciliation, deposits in transit are: (a) deducted from the book balance. (b) added to the book balance. (c) added to the bank balance. (d) deducted from the bank balance.
Sustainability involves more than just the impact of actions on the environment. The triple bottom line recognizes that a company has to measure its impact on people, planet, and profit for its long-...
Refer to the information for Deporte Company above. Deporte Company produces single-colored t-shirts. Materials for the shirts are dyed in large vats. After dying the materials for a given color, the...
3.5
Elmbrook Corporation reported net income of $58,000. Depreciation expense for the year was $132,000. The company calculates depreciation expense using the straightline method, with a useful life of...
i just need to know the return on total assets Comparative financial statements for Weller Corporation, a merchandising company, for the year ending December 31 appear below. The company did not...
A gear reduction unit uses the countershaft shown in the figure. Gear A receives power from another gear with the transmitted force FA applied at the 20_ pressure angle as shown. The power is...
Problems 47 through 49 develop properties of matrix transposes. Suppose that A and B are matrices of the same size. Show that: (a) (A T ) T = A; (b) (CA) T = CA T ; and (c) (A + B) T = A T + B T .
Suppose that A 2 = A. Prove that |A| = 0 or |A| = 1.
In Problems 5378, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you...
Analysis of the Volkswagen Scandal Possible Solutions for Recovery The Volkswagen scandal is a notorious example of how corporations can shape the ethical and political issues of the environment. The...
Shelby isn't sure if her forklift can safely handle the pallet she is being asked to move. What can she check to be sure
If schedule acceleration increases costs, how could schedule elongation reduce costs? If schedule acceleration increases costs, how could schedule elongation reduce costs? For the same total...
Laser Care Hospital is looking to raise tax-exempt municipal funds in the bond market. As an issuer of the bond, which of the following is not a part of the bond process that Laser Care Hospital will...
Find the critical value t a/2 corresponding to a 95% confidence level. (13.046, 22.15) X= 17.598 Sx= 16.01712719 n=50
Suppose that a firm's marginal production costs are given by MC = 10 + 30Q. The firm's production process generates a toxic waste, which imposes an increasingly large cost on the residents of the...
Give an example of transitory income. What effect does this income have on the marginal propensity to consume?
Explain what a reversal design?
How does a multiple-baseline design differ from a reversal design?
Give three reasons a researcher might choose to use a single-case design.
explain in excel please For a particular product the price per unit is $6. Calculate Revenue if sales in current period is 200 units. Conduct a data analysis, on revenue by changing the number of...
Hall Company sells merchandise with a one-year warranty. In the current year, sales consist of 35,000 units. It is estimated that warranty repairs will average $10 per unit sold and 30% of the...
Q 4- Crane Corporation, an amusement park, is considering a capital investment in a new exhibit. The exhibit would cost $ 167,270 and have an estimated useful life of 7 years. It can be sold for $...

Let A = [a ij ] be a 3 x 3 matrix. Show that det(A T )

Question:

Step by Step Answer:

If we write then expansion of A ...View the full answer

Differential Equations And Linear Algebra

Students also viewed these Mathematics questions