Let V be the set of all 2 x 2 matrices (a) Is V closed under addition?

Question:

Let V be the set of all 2 x 2 matrices

(a) Is V closed under addition?
(b) Is V closed under scalar multiplication?
(c) What is the zero vector in the set V?
(d) Does every matrix A in V have a negative that is in V? Explain.
(e) Is V a vector space? Explain.

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

Step by Step Answer:

Related Book For book-img-for-question

Elementary Linear Algebra with Applications

ISBN: 978-0132296540

9th edition

Authors: Bernard Kolman, David Hill

See More Books

Question Posted: Jun 21, 2016 07:03 AM

See More Questions

Let V be the set of all infinite sequences (a0, a1, a2,...) of real numbers. Define addition and scalar multiplication by (a0, a1,...) + (b0, b1,...) = (a0 + b0, a1 + b1,...) and r(a0, a1,...) =...
Let V be the set of all polynomials of (exactly) degree 2 with the definitions of addition and scalar multiplication as in Example 6. (a) Show that V is not closed under addition. (b) Is V closed...
Let W be the set of all 2 ( 2 matrices Such that Az = 0, where Is W a subspace of M22? Explain. A s d
1. What is Ladures target market and retail strategy in the United States? 2. Explain the reasons Ladure owns its stores in some countries and uses franchising with local licensees in others. 3....
Refer to the previous question. Suppose plants 1 and 2 represent different building alternatives for the same site (that is, only one of these plants can be built). Similarly, suppose plants 4 and 5...
Powell owns a 20 percent interest in Cooke Partnership. At the beginning of 2019, Powells basis is $22,000. Cooke reports a $90,000 operating loss in 2019, and Powell withdraws $10,000 from the...
Construct a binomial tree $\left(u=\frac{1}{d} ight)$ with three quarters for an asset with present value $\$ 100$. If $r=0.1$ and $\sigma=0.4$, using the tree compute the prices of: (a) A...
Multiple Choice Questions Select the best answer for each of the following questions. Explain the reason for your selection. a. Which of the following would be least likely to be considered an...
A set S R^n is convex if for all x, y S and t [0, 1], we have (1 t)x + t y S (in other words, if S contains the points x and y, it contains the entire line segment between them). (a) If W R^n is a...
Find a Doctor is a small startup that helps people find a physician who best meets their needs (location, insurance accepted, etc.). During a slow time for it, it has seven staff members taking calls...
Let W be a nonempty subset of a vector space V. Prove that W is a subspace of V if and only if ru + sv is in W for any vectors u and v in W and any scalars r and s.
Prove in detail that Rn is a vector space?
Electrical resistance heaters are usually made from coils of nichrome wire. The coiled wire can be supported between insulators and backed with a reflector, for example, as in a supplemental room...
Assume that you are the Human Resource (HR) Director of an Australian company that has begun international assignments in the UAE. You are considering using an external consulting firm to provide...
Let h > 0 and C (R). Show there exists x0 = [x,x+h] where f(x + h) f(x) - f'(xo) - = kh f(3) () h where = (x, x + h) and k < 0.
#2: An annuity has payments at the beginning of every three months starting today. The first payment is $100 and payments increase by 1% every three months for the first four years, making the 16th...
Let G = (V,E) be a graph. Consider variables xe associated with each edge e E. Let P(G) be the polytope given by: eed(v) e 1 \v V Xe 0 Ve EE We showed in class that if G is bipartite, then all...
Problem 5. (3+1+2+6 points) Let y be the boundary of the rectangle with vertices at the points 1-i, 1+2i, 1+2i, -1- i oriented in the counterclockwise direction around the origin. (a) Drawy and find...
Refer to the information in Exercise 21-11. 1. Compute the companys degree of operating leverage. 2. If sales decrease by 5% in the next year, what will be the companys income? 3. Prepare a...
Convert the numeral to a HinduArabic numeral. A94 12
Let C3 have the Euclidean inner product. For which complex values of k are u and v orthogonal? u = (2i, i, 3i), v = (i, 6i, k)
Let C3 have the Euclidean inner product. Show that for all values of the variable Î¸, the vector has norm 1 and is orthogonal to both (1, i, 0) and (0, i, - i). -,-() 3
Let C3 have the Euclidean inner product. Which of the following form orthonormal sets? 0.4-) (4-4-4) (4-0 )
Consider a plane of mass 50,000 kg in takeoff when the thrust for each of its four engines is 25,000 N. If the plane is facing an air drag force of 10,000 N; What is the acceleration of the plane?
Discuss the rationale and ways in which developers are regulated in relation to the acquisition and development of land in Singapore.
Interview an individual who has a chronic illness. With the individual's permission, interview them about what it is like to live with a chronic illness, the most difficult parts of being chronically...

Let V be the set of all 2 x 2 matrices (a) Is V closed under addition?

Question:

b7

Step by Step Answer:

a No b Yes c d Yes If Then a...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions