If A is a 2 2 matrix, show that its eigenvalues satisfy the characteristic equation

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

Question:

If A is a 2 × 2 matrix, show that its eigenvalues λ satisfy the characteristic equation

Related Book For answer-question

Linear Algebra With Applications

ISBN: 9780070985100

7th Edition

Authors: W. Keith Nicholson

See More Books

Posted Date: Oct 04, 2022 11:18 AM

See More Questions

If A is a 2 Ã 2 matrix with eigenvalues Î»1 = ½, Î»2 = - 1, and corresponding eigenvectors Find 2 -37
If A is any 2 Ã 2 matrix, show that: for some numbers p, q, r, and s. I 01 0 1 A=p 1 0 1 0
A matrix A has eigenvalues -1 and 2 and associated eigenvectors Write down the matrix form of the linear transformation L[u] = A u in terms of (a) The standard basis e1, e2; (b) The basis consisting...
A company writes a check to replenish a $100 petty cash fund when the fund contains receipts of $94 and $4 in cash. In recording the check, the company should: (a) debit Cash Over and Short for $2....
Grace, the minister of the local United Methodist Church, has some tax questions regarding her employment status. This is her first year as a United Methodist minister after having served as a...
Look again at Solved Problem 29.3, where the saving and investment equation S = I + NX is derived. In deriving this equation, we assumed that national income was equal to Y. But Y only includes...
What are the differences between equitable and legal remedies? Identify two types of equitable remedies.
You have a $10 million capital budget and must make the decision about which investments your firm should accept for the coming year. Projects 1, 2, and 3 are mutually exclusive, and Project 4 is...
Starting with the base case below, let's say a restaurant implements a lean op's initiative such that it is able to increase capacity (the maximum throughput rate) by 5% without an increase in fixed...
Katsura Corporation incurred pre-operating costs: Investigatory expenses of $17,000 New employee training $25,000 Advertising $10,000 Land and building for use as a retail store when opened...
Differentiate. When appropriate, you might consider first simplifying the expressions before differentiating. For example, In(a b) In a + lnb or ln(a) = bln a. 1. f(x) 2. f(8) = In x+1 with respect...
Pick a brand that you currently use. Check the brands presence on Twitter. See how far you can go in learning about the brand. For example, how many hashtags are used that pertain to the brand? If...
Define current assets and give three examples.
The CFO Magazine in the USA publishes information to help chief finance officers (finance directors) in companies. The following information is extracted from its annual Working Capital Survey. For...
Do male and female communication patterns differ regarding verbal dominance?
Have you ever used resistance strategies? Did they work?
Hairdecor Company sells decorative headbands to retailers for $7.50. The variable cost of goods sold per headband is $1.50, with a selling commission of 15 percent. Fixed manufacturing costs total...
In 1995 Miguel purchased a home for $130,000. In 2000 he sold it for $170,000 and immediately purchased another one for $180,000, which he sold in 2007 for $235,000. How much taxable capital gain, if...
Let U and W be subspaces of Rn. Define their intersection U W and their sum U + W as follows: U W={X in Rn | X belongs to both U and W}. U+ W= {X in Rn | X is a sum of a vector in U and a vector in...
Show that the real system has a complex solution: x = 2, y = i, z = 3 - i where i2 = -1. Explain. What happens when such a real system has a unique solution? x+ y+ z=5 -3x + 2y + 2z = 0
Consider the letter 4 described in Figure 4.38. Find the data matrix for the letter obtained by: Rotating the letter through Ï/4 about the point
If the least-squares regression line has slope b1 = 5, and two x-values differ by 3, the predicted difference in the y-values is _____________________. In Exercises 57, fill in each blank with the...
For each of the following plots, interpret the y-intercept of the least-squares regression line if possible. If not possible, explain why not. a. The least-squares regression line is = 1.98 +...
Substituting the value of the explanatory variable for x in the equation of the least-squares regression line results in a prediction for y. In Exercises 812, determine whether the statement is true...

If A is a 2 2 matrix, show that its eigenvalues satisfy the characteristic equation

Question:

A² Atr(A)+det(A) = 0 A² Atr(A)+det(A) = 0

Expert Answer:

Leta 202 maharin A and asing Characteristic equation 14 23 5 33 3... View the full answer

Linear Algebra With Applications

Students also viewed these mathematics questions