Let A be a nonsingular n n matrix and let be an eigenvalue of A.
Question:
(a) Show that λ ≠ 0.
(b) Show that 1/λ is an eigenvalue of A-1.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 60% (15 reviews)
a det A 1 2 n If A is nonsingular then det A 0 and hence all of ...View the full answer
Answered By
Loise Ndungu
I have five years of experience as a writer. As I embark on writing your papers from the prologue to the epilogue, my enthusiasm is driven by the importance of producing a quality product. I put premium product delivery as my top priority, as this is what my clients are seeking and what makes me different from other writers. My goal is to craft a masterpiece each time I embark on a freelance work task! I'm a freelance writer who provides his customers with outstanding and remarkable custom writings on various subjects. Let's work together for perfect grades.
4.90+
78+ Reviews
224+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
Let A be a nonsingular n n matrix. Use mathematical induction to prove that Am is nonsingular and (Am)-1 = (A-1)m for m = 1, 2, 3, ...
-
Let A be a nonsingular n n matrix and let B be an n r matrix. Show that the reduced row echelon form of (A|B) is (I|C), where C = A-1B.
-
Let A be a nonsingular n n matrix with n > 1. Show that det(adj A) = (det(A))n-1
-
An investment project has annual cash inflows of $3,200, $4,100, $5,300, and $4,500, and a discount rate of 14 percent. What is the discounted payback period for these cash flows if the initial cost...
-
The merchandise inventory was destroyed by fire on May 17. The following data were obtained from the accounting records: a. Estimate the cost of the merchandise destroyed. b. Briefly describe the...
-
A tank (Figure P1.11) with mass \(m_{1}=2,000 \mathrm{~kg}\) fires a cannon with mass \(m_{2}=2 \mathrm{~kg}\) and velocity \(=10 \mathrm{~m} / \mathrm{sec}\). The recoil mechanism consists of a...
-
List some of the important additional requirements for a successful VM implementation.
-
On July 1, Coastal Distribution Company is considering leasing a building and buying the necessary equipment to operate a public warehouse. Alternatively, the company could use the funds to invest in...
-
A loan of 20,000 is repaid by a payment of X at the end of eachyear for 10 years. The loan has an annual effective interest rateof 11% for the first 5 years and 12% thereafter. Calculate X. Showthe...
-
The truss shown consists of nine members and is supported by a ball and socket at B, a short link at C, and two short links at D. (a) Check that this truss is a simple truss, that it is completely...
-
Let A be a 4 4 matrix with real entries that has all 1's on the main diagonal (i.e., a11 = a22 = a33 = a44 = 1). If A is singular and 1 = 3 + 2i is an eigenvalue of A, then what, if anything, is it...
-
Show that if A is a matrix of the form then A must be defective. Ola 0a0 a)0
-
If df Between = 3, df Within = 17, F = 5.34, and = .05, write the results in APA format. (Use df Between and df Within to find F cv in order to determine if the null hypothesis was rejected.)
-
Nintendo of America, Inc. contacts Play 2 Win Games and offers to sell one to twenty-five new gaming systems for $75 each. State number desired in acceptance. Play 2 Win agrees to buy twenty systems....
-
RiotGear contracts with Standard Transit, Inc., to distribute RiotGears Occupy Earth/Global Movement line of apparel to retail outlets for a certain price. With the goods in transit, RiotGear...
-
RiotGear promises to donate a share of the proceeds from the sale of the Occupy Earth/Global Movement line to The Cause, a charitable organization dedicated to supporting those who seek social and...
-
Roberto, who did not speak or read English, visited Dart Dodge, a car dealership. Aware that Roberto was monolingual, Darts staff transacted a deal in Spanish. They explained the English-language...
-
Lianna Saribekyan placed diamonds, gold, and other collectibles in her safe deposit box at the Bank of Americas (BANAs) Universal City, California, branch. When this branch was slated for closure,...
-
Toasters again In a batch of 10,000 toasters, what are the chances that fewer than 450 need to be returned?
-
During the year land was revalued and the surplus reported as Revaluation surplus; and an asset costing 80,000, written down to 38,000, was sold for 40,000. Identify the cost of any non-current...
-
Let L1 and L2 be linear transformations from a vector space V into a vector space W. Let {v1, v2 ... vn} be a basis for V. Show that if L1 (v,) = L2 (v) for i = 1, 2 . . . n, then L1 (v) = L2 (v) for...
-
Let L: V W be a linear transformation from a vector space V into a vector space W. The pre-image of a subspace W1 of W is defined as
-
Let O: Rn Rn be the zero linear transformation defined by O (v) = 0 for v in Rn. Find the standard matrix representing O.
-
The highest WACC is 11%, the baseline WACC is 7.4% and lowest WACCS is 2.8%. To derive a WACC that better accounts for extreme scenarios, you decide to assign the following probability weights: High-...
-
Give 2 examples of the ff: Statutory law Regulatory law Common law Include the title of each example and explain why you chose these examples ( 1 to 2 sentences ) . Note: Write your reference ( s )
-
The Adams family includes a financially well-informed couple, both aged 36, and two children aged 4 and 6. The family is financially sound but suffered badly during the tech meltdown in 2000. The...
Study smarter with the SolutionInn App