Hi. I have two questions about the linear algebra. 1. Consider the following sets: (a) The...

Hi. I have two questions about the linear algebra.

1. Consider the following sets:

(a) The set f all diagonal 3*3 matrices

(b) The set of all vectors in R^4 whose entries sum to 0.

For the cases where the set is a vectors space, give the dimension and a basis

********************************************************

2. Let L be the set of all linear transforms from R^3 to R^2

(a) Verify that L is a vector space.

(b) Determine the dimension of L and give a basis for L.

Will thumb up for both answers. Thank you so much.

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Linear Algebra Conceptual Questions • What are the possible sizes of solution sets for linear systems?...

Linear Algebra Conceptual Questions • What are the possible sizes of solution sets for linear systems? • List as many things that are equivalent to a square matrix being nonsingular as you can. • List as many things that are equivalent to a square matrix being singular as you can. (Should be basically the same as your list above except all opposites) • Give an example of a singular matrix that is NOT just the zero matrix. • If a...

Hi, I have some doubs about answers to following questions and I apprecite if someone could...

Hi, I have some doubs about answers to following questions and I apprecite if someone could help me with the answers: We want to investigate the following research problem: We have been developing a new learning and teaching application and want to know if this application is more efficient on a tablet or on a mobile phone. Efficiency is measured in the speed in which answers in the form of text are entered. i. Formulate the hypothesis H1 and the...

Linear algebra confusion: We haven't learned about rank and such: For the following I am looking...

Linear algebra confusion: We haven't learned about rank and such: For the following I am looking for examples or checking to see why something is impossible. a.) What does it mean when we have an inconsistent 2x3 linear system -What if we reversed it to 3x2? Even put other numbers in place. b.) Can a 2x3 linear system have a unique solution -What if we reversed it to 3x2? Even put other numbers in place. c.) Can a 3x2 linear...

I have to write report about Application of Linear Algebra in Electronic Engineering. Let me know...

I have to write report about Application of Linear Algebra in Electronic Engineering. Let me know about the examples simply and variously as possible as you can.

Hi, I have some questions about the concepts of energy in chemistry. #1 A particular chemical...

Hi, I have some questions about the concepts of energy in chemistry. #1 A particular chemical reaction has a negative deltaH and a negative deltaS. Which statement is correct? The answer: -The reaction becomes spontaneous as temperature decreases. Can someone please explain to me how this is true? #2 For the process O2(g)---> 2O(g), deltaH = +498kJ. What would be predicted for the sign of deltaS(rxn) and the conditions under which this reaction would be spontaneous? The answer: deltaS(rxn)=positive &...

LINEAR ALGEBRA Prove or disapprove (no counterexamples): Given that sets A = {u1....un} and B =...

LINEAR ALGEBRA Prove or disapprove (no counterexamples): Given that sets A = {u1....un} and B = {v1....vn} are subsets vectors of a vector space V. If the vectors in A and B, respectively, are independent and dim(Span(u1....un)) = dim(Span(v1....vn)) then Span(u1....un) = Span(v1....vn)

Can i please have a quick explanation on Markov Chain in linear algebra. Thanks

Hi, I'm currenlty learning about Forex trading(CANADA). I have a couple of questions of they could...

Hi, I'm currenlty learning about Forex trading(CANADA). I have a couple of questions of they could be answered: 1.) What are the fee's involved with CFD's and FX markets. 2.) what are the costs of keeping a stock over night what the fee's would be on that.

Consider the general linear model ? = ?? + ?. Use matrix algebra to show that...

Consider the general linear model ? = ?? + ?. Use matrix algebra to show that ?̂ is an unbiased estimator of ?. the last ? has bar

What are the two parts of the Fundamental Theorem of Linear Algebra?

What are the two parts of the Fundamental Theorem of Linear Algebra? How can they be applied? Give 1 example problem for each part.

Subjects