Question
Asked Oct 8, 2019
14 views

See picture

a basis for M2(R)? Explain why
why not
4. Is L
or
help_outline

Image Transcriptionclose

a basis for M2(R)? Explain why why not 4. Is L or

fullscreen
check_circle

Expert Answer

Step 1
A subset L C M2(R) is a basis of M2(R) if any vector v E M2(R) is uniquely represented as
linear combination
a
where vi, Vi,. are distinct vectors from M2(R) and xi, x, ..., XE R
www.
here dim(Mz2(R)} = 4
а, b
М,
с, d,
ab
help_outline

Image Transcriptionclose

A subset L C M2(R) is a basis of M2(R) if any vector v E M2(R) is uniquely represented as linear combination a where vi, Vi,. are distinct vectors from M2(R) and xi, x, ..., XE R www. here dim(Mz2(R)} = 4 а, b М, с, d, ab

fullscreen
Step 2
dim M22(R) 4 so if satisfied to show that the given basis is linearly independent
By the definition of the basis for every subset of M2(R).aud every x1, x2, ..., Xa in R. if
Xn Xa 0 then necessarily x
xao= X= 0
XIV1X2V2
O 0
1 0
0 1
х,
1 1
1
x, +
0 0
1
x, +
1
0 1
1
0
_,+x, x,+x, +x
0
help_outline

Image Transcriptionclose

dim M22(R) 4 so if satisfied to show that the given basis is linearly independent By the definition of the basis for every subset of M2(R).aud every x1, x2, ..., Xa in R. if Xn Xa 0 then necessarily x xao= X= 0 XIV1X2V2 O 0 1 0 0 1 х, 1 1 1 x, + 0 0 1 x, + 1 0 1 1 0 _,+x, x,+x, +x 0

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Advanced Math

Related Advanced Math Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: b

A: The given equation is of the form y’+ P y = Q yn , n is not equal to 0,1. Where P and Q are constant...

question_answer

Q: what is the product of 9/11 and it's reciprocal

A: The given fraction is 9/11.The reciprocal of the number is 1 / (9/11).That is, 11/9.

question_answer

Q: 1. Let V be an inner product space. Suppose f,g E V such that f -gg (a) Prove that 1I2 = |lf- gll2 +...

A: To prove the required norm property in an inner product space, under the given conditions

question_answer

Q: Assume that 4 digits are selected at a random from the set { 1,2,3,4} and are arranged in random ord...

A: The set of the digits from which the digits are selected randomly and arranged in random order is

question_answer

Q: What is the fibonacci sequence?

A: Fibonacci sequence are the numbers that have the following sequence.1,1,2,3,5,8,13,21,34,55,89,144….

question_answer

Q: You are portioning out bread dough. How many full 17-ounces portions can be obtained from 15.5 kilog...

A: The problem is to keep track of the different systems of units (ounces and kilograms) and their conv...

question_answer

Q: 4. Let E CRd, and for each nE N, define On as the set On z d(x, E) 1/n) Recall that d(x, E) inf{| - ...

A: To prove the openness of the given sequence of sets

question_answer

Q: Please help me problem 1(a), please as clear as possible for the proof

A: Given:

question_answer

Q: Solve the given initial-value problem. (Assume  ω ≠ γ.) d2x dt2 + ω2x = F0 cos(γt),  x(0) ...

A: Find the homogeneous solution of the given IVP as follows.