Question: For each subspace, (a) Find a basis (b) State the dimension {(a, b, c, d): a-3b + c = 0}

For each subspace,


(a) Find a basis


(b) State the dimension


{(a, b, c, d): a-3b + c = 0}

{(a, b, c, d): a-3b + c = 0}

Step by Step Solution

★★★★★

3.31 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

We are given the subspace abcd a 3b c 0 To find a basis we need to find a set of linearl... 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 Linear Algebra And Its Applications Questions!

Q:

For each subspace below find a basis for the subspace and state the dimension of the subspace. {(a, b, c) = R | a 3b + c = 0} - {(a, b, c) = R | a a 3b + c = 0, b2c=0, 2bc=0}

Q:

Find the dimension of and a basis for the subspace spanned by the following sets of vectors. (a) (b) (c) (d) (e) 121 3 1233 2210 1001 1010 90000 13121 034011 21221 10320

Q:

Find the dimension of the subspace of M2,2. a gila.+ b = c, b + c = d, c + d a

Q:

Let V = P(4) denote the space of quartic polynomials, with the L2 inner product Let W = P2 be the subspace of quadratic polynomials. (a) Write down the conditions that a polynomial p P(4) must...

Q:

2.39 Consider the vector space S = {u : u = Ax,x R*}, where A is the 4 x 4 matrix given by [1 2 1 1 A = 1 0 2 2 4 3 1 3 -2 0 PROBLEMS 89 (a) Determine the dimension of S and find a basis. (b)...

Q:

Question 2 (20 marks) a. Let S be the set of matrices of the form 05h b r: ' where a, b, and c e R. The vector addition and scalar multiplication in S are the usual Operations of matrix addition and...

Q:

7 Steps for Tests of Significance 1. State the research question. 2. Identify the parameter. 3. State the hypotheses. 4. Choose the method. 5. Do the test. 6. Interpret the p-value and alpha. Must be...

Q:

7 Steps for Tests of Significance 1. State the research question. 2. Identify the parameter. 3. State the hypotheses. 4. Choose the method. 5. Do the test. 6. Interpret the p-value and alpha. Must be...

Q:

Question 1 Let U be the set of vectors (:13, y, 1) with a: and yin R. Determine whether or not U is a subspace of R3. The set U: [3 includes the zero vector is closed under vector addition is closed...

Q:

please help to answer these 8 questions, thank you~ Question 1. In each of the following, determine if the given set is a subspace of R2 or not. For each case in which the set is a subspace, verify...

Q:

Congress should pass a law forbidding corporations to keep two sets of books. Do you agree? Explain.

Q:

Lambda Corporation has current liabilities of $450,000, a quick ratio of 1.8, inventory turnover of 5.0, and a current ratio of 3.5. What is the cost of goods sold for Lambda Corporation?

Q:

According to federal regulations related to the opening of a customer account, the Customer Identification Program (CIP) requires what minimum information about the customer? QID: 5191385Mark For...

Q:

15. Let X1, X2, . . . , Xn represent a random sample from a Rayleigh distribution with pdf f(x; ) x e x2/(2) x 0 a. It can be shown that E(X2 ) 2. Use this fact to construct an unbiased estimator...

Q:

A law enforcement agency, administering breathalyzer tests to a sample of drivers stopped at a New Years Eve roadblock, measured the following blood alcohol levels for the 25 drivers who were...

Q:

According to the Energy Information Administration, the average U.S. household spends $1338 per year for utilities (including heat, electricity, cooling, and water). The averages by region were as...

Q:

Brides magazine reports the cost of the average honeymoon as $3657. Assume that their findings could have been based on the honeymoon expenditures of a sample consisting of 300 couples whose costs...

Q:

solutions to exercise 20 and problem 5 of chapter 14 in the intermediate accounting textbook, 13th edition

Q:

Financial information is presented here for two companies. Fill in the missing amounts. Iwig Company Pratt Company Sales $135,000 $ Sales returns $ $7,500 Net sales $121,500 $150,000 Cost of goods...

Q:

A 20-year, $1,000 par value bond has a 7.50% coupon rate with interest paid semiannually. The bond currently sells for $850. What is the capital gains yield on these bonds? Enter your answer rounded...