Prove that if A is nonsingular then AT is nonsingular and (AT)-1 = (A-1)T
Question:
(AT)-1 = (A-1)T
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 58% (17 reviews)
Since A T A 1 T ...View the full answer
Answered By
Michael Owens
I am a competent Software Engineer with sufficient experience in web applications development using the following programming languages:-
HTML5, CSS3, PHP, JAVASCRIPT, TYPESCRIPT AND SQL.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
Provide an alternative for the second half of the proof of Theorem NMUS, without appealing to properties of the reduced row-echelon form of the coefficient matrix. In other words, prove that if A is...
-
Show that if A is nonsingular then adj A is nonsingular and (adj A)-1 = det(A-1)A = adj A-1
-
Let A be an m x n matrix with rank A = n. (a) Prove that the matrix P = A(ATA)~l AT is a projection matrix, meaning that P2 = P, cf. Exercise 2.5.8. (b) Construct the projection matrix corresponding...
-
Explain how the structure of the balance sheet corresponds to the accounting equation.
-
Springer County Bank has assets totaling $180 million with a duration of five years, and liabilities totaling $160 million with a duration of two years. If interest rates drop from 9% by 75 basis...
-
The Metropolis Public Library plans to expand with its first major branch library in the citys growing north side. The branch will serve six census tracts. Here are the coordinates of each tract and...
-
Why does the form of an occurrence affect the auditor's interpretation of sample results?
-
The standard cost of Product B manufactured by Pharrell Company includes three units of direct materials at $5.00 per unit. During June, 29,000 units of direct materials are purchased at a cost of...
-
Here my is papr i have gathered information help expand more the questions to papr 5 pg. Our coffee shop chain expansion plan is comprehensively designed to enhance productivity, improve competitive...
-
Richard chooses technique 0 and 2 requiring 10+10-20 efforts and provising 10+11=21 benefits. Hence, 21 is returned as the output Example 2: input1: 3 input2: (10,10,10,10) input3: (10,11,12,15)...
-
Let Show that if d = a11a22 - a21a12 0, then A=[2:22] a2i 22 a22 -a12 d -a a 421 41)
-
Let A be an n n matrix and let x and y be vectors in Rn. Show that if Ax = Ay and x y, then the matrix A must be singular.
-
Why do the rates of chemical reactions increase dramatically with increasing temperature?
-
Traditional free-trade theory is basically a static theory of international exchange leading to certain conclusions about the benefits likely to accrue to all participants. Explain the dynamic...
-
Why do you think conflicts within developing countries increased so much from the 1950s to the 1990s? Why do you think they then began to decrease?
-
Describe Kuznetss inverted-U hypothesis. Discuss the conceptual merits and limitations of this hypothesis for contemporary developing countries.
-
Why is development participation not used more often despite its potentially decisive role in ensuring the success of development policies?
-
For many years, the conventional wisdom of development economics assumed an inherent conflict between the objectives of maximizing output growth and promoting rapid industrial employment growth....
-
Carroll Company, a manufacturer of vitamins and minerals, has been asked by a large drugstore chain to provide bottles of vitamin E. The bottles would be labeled with the name of the drugstore chain,...
-
As you rewrite these sentences, replace the cliches and buzzwords with plain language (if you don't recognize any of these terms, you can find definitions online): a. Being a jack-of-all-trades, Dave...
-
Let A be the matrix Determine whether A is invertible, and if so, find its inverse. 101 011 110
-
Apply parts (d) and (m) of Theorem 1.4.1 to the matrices A, B, and (-1) C to derive the result in part (f).
-
Consider the laws of exponents Ar As = Ar+s and (Ar)s = Ars. (a) Show that if A is any square matrix, then these laws are valid for all nonnegative integer values of r and s. (b) Show that if A is...
-
You invest into Malaysian stock market. On 3 May 2021, construct an investment portfolio. State the reason(s) for selecting those financial assets available in the Malaysian stock market. (b) To...
-
Control Substances: 3.0 g calcium carbonate (chalk) and 0.50 M HCI CaCO3(s) + 2HCl(aq) CaCl2(s) + H2O(aq) + CO2(g) Can you please 2 graphs, one for the control experiment and one for the variable...
-
Calculate the payback and NPV for a project with a $100,000 initial cost, cash inflows of $35,000 per year for 4 years, and a discount rate of 12%?
Study smarter with the SolutionInn App