Question: Show that A -1 exists if and only if the eigenvalues 1 , , n are all nonzero, and then A

Show that A-1 exists if and only if the eigenvalues λ1, · · ·, λn are all nonzero, and then A-1 has the eigenvalues 1/λ1, · · ·,1/λn.

Step by Step Solution

★★★★★

3.43 Rating (156 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

By Theorem 1 in Sec 78 the inverse exists if and only if det A 0 On the oth... 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

Students Have Also Explored These Related Advanced Engineering Mathematics Questions!

Q:

The left-hand and right-hand derivatives of f at are defined by if these limits exist. Then f'(a) exists if and only if these one sided derivatives exist and are equal. (a) Find f'-(4) and f'+(4) for...

Q:

a. Suppose that f: (0, 1) R is a non-negative continuous function. Show that (0, 1) exists if and only if lim Є c 1-c f exists. b. Let An = [1 - 1/2n, 1 - 1/2n +1] Suppose that f: (0, 1) R...

Q:

Show that the inverse A1 exists if and only if none of the eigenvalues 1, , n of A is zero, and then A1 has the eigenvalues 1/ 1, , 1/n.

Q:

CONCEPTS 9. 1' + 2 + 3 3 + . . . + 1) = n (n + 1)2 1. Mathematical induction is a method of proving that a statement 4 P(n) is true for all numbers n. In Step I we prove 10. 13 + 3 + 53 + . .. + (2n...

Q:

1. (a) Show that 27 1 1 n-2 log|2| if n = 2, n(x) = if n e N, n > 3. n(n-2)vol(B1(0)) solves the Laplace equation in R\{0}. (b) Given f C2(R3) with compact support show that u(t) = n(y x)f(y)dy...

Q:

Kindly explain the following 12. A monopolist has a single production plant in California with a total cost function of c(Q) = =Q2, where Q is total output. The good can be sold to two separate...

Q:

Questions & Exercises 1. A primitive in one context might turn out to be a composite of primitives in another. For instance, our while statement is a primitive in our pseudo- code, yet it is...

Q:

Let w be the complex number (1/2) (1 + i). (a) Show that w8 = 1 but of wn 1 for n Z+, 1 n 7. (b) Verify that [wn|n Z+, 1 n 8] is an abelian group under multiplication.

Q:

Give the asymptotic running time of each the following functions in notation. Justify your answer. (Show your work.) 1. func1(n) 1 s+0; 2 for i + 100 to n do for j+ 11 to [i/3 (log7(i))] do |s+s+i j;...

Q:

Help with this question from casella and berger? 10.18 For the situation of Exercise 10.2.1, that is, if X1, X2, ..., Xn are iid, where Xi ~ n(u, 2) with probability 1 -8 and X, ~ f(r) with...

Q:

For the process shown . step 1 step 2 step 3 3 min / unit 5 min / unit 2 min / unit What is the process capacity (in hours)? Tbnmmen.coy ob osi ate What is the flow rate if the demand is 10 units per...

Q:

According to Mediaweek, there are three methods of advertising on the Web. Method 1 is to serve ads to users who clicked on an icon for the ad; Method 2 serves ads through visits to the company's Web...

Q:

33. LO.6 If the beginning balance in Strauder, Inc.s OAA is $5,700 and the following transactions occur, what is Strauders ending OAA balance? Depreciation recapture income $22,700 Payroll tax...

Q:

6. Select a price you are willing and able to pay for each purchase. List the prices in the Spending Limit column of the table

Q:

Answer Problem 3.40 for families with two male siblings? Suppose that a disease is inherited via a sex-linked mode of inheritance. The implications of this mode of inheritance are that each male...

Q:

Answer Problem 3.41 for families with two male siblings? Suppose that a disease is inherited via a sex-linked mode of inheritance. The implications of this mode of inheritance are that each male...

Q:

Answer Problem 3.42 for families with two male siblings? Suppose that a disease is inherited via a sex-linked mode of inheritance. The implications of this mode of inheritance are that each male...

Q:

PRICE SHARES Company A B C A B C Day 1 $12 $24 $54 450 380 220 Day 2 11 21 55 450 380 220 Day 3 14 48 60 450 190a 220 Day 4 11 46 29 450 190 440b Day 5 12 46 30 450 190 440 aSplit at close of day 2....

Q:

1. Say we have a simple linear regression with a single response Y and a single quantitative covariate X. The population model is: Y; = 60 + 61X\"; + 53-. An observation of X, say X,, is considered...

Q:

The following table presents the long-term liabilities and stockholders equity of Information Control Corp. one year ago: Long-term debt $ 66,200,000 Preferred stock 4,120,000 Common stock ($1 par...