linear algebra

Question

Question

Determine whether the following subset W = {(a, b, c)| a, b, c are rational numbers} is a

subspace of V = R^3 or not. Please explain.

Answer 1

Similar Homework Help Questions

How do I do these linear algebra questions? The question is: Consider the Vector Space V...

How do I do these linear algebra questions? The question is: Consider the Vector Space V and its subset W given below. Determine whether W forms a subspace of V. If your answer is negative then you must provide which subspace requirement is violated. (b). V is P5, the vector space of all polynomials in x of degree s5 and W is the set of all polynomials divisible by x – 3. (c). V is P5, the vector space of...
8 and 11 Will h x n lower triangular matrices. Show it's a w It's a...

8 and 11 Will h x n lower triangular matrices. Show it's a w It's a 8. Dan will represent the set of all n x n diagonal matrices. Show it's a subspace of Mr. 9. For a square matrix AE M , define the trace of A, written tr(A) to be the sum of the diagonal entries of A (i.e. if A= a) then tr(A) = 211 + a2 + ... + ann). Show that the following subset of...
Help with the following Linear Algebra questions as many as possible: Name There are 10 questions...

Help with the following Linear Algebra questions as many as possible: Name There are 10 questions worth 10 points each. Feel free to discuss these exercises with your classmates but please write each solution in your own words. Please include all the details necessary to explain your work to someone who is not necessarily enrolled in the course. 1) Show that there is no matrix with real entries A, such that APEX 11 a 001 2) Find the inverse of...

PART 2: Assorted Problems. Show all work for full credit. (8) 1. In each of the...

PART 2: Assorted Problems. Show all work for full credit. (8) 1. In each of the following, determine whether or not the subset W of the vector space Vis a subspace of V. Justify your conclusions. a. V-Mn: W the set of all 2x2 matrices with rational number entrics b. VP: W-the set of all polynomials a, +ar+a in where a, +a, -2a, -o. (b) 2. Find elementary matrices E,E, such that EA-B and E,B-A when 2 7 3 8...
Since it was multiple choice with only two answers, I was able to guess which one...

Since it was multiple choice with only two answers, I was able to guess which one it was but I need to know how to show it on paper. If the image is too small: Let V be a vector space and let W be a nonempty subset of V. Then W is a subspace of V if and only if the following conditions hold. (a) If u and v are in W, then u + v is in W....
Let V be a vector space and W be a subset of V. By justifying your...

Let V be a vector space and W be a subset of V. By justifying your answer, determine whether W is a subspace of V. (a) V = M2,2 and EV : ad = bc (b) V = P3 and W = {a + bx + cx? + dx€ V: a+c= b+d}. +

Linear Algebra Question: Forgot to include the vaules of u, v and w.

Linear Algebra Question: Forgot to include the vaules of u, v and w. :]suchthata,b,c,dso 6. 18 Points] Show that V, the set of all 2x2 matrices of the form such that a, b, c, d s0, is not a subspace. s. I5 Points each] Let ü = (2,-6, 2), v = (0, 4,-2), and w-(2, 2,-4) a. Find a vector that is orthogonal to both v and w using the cross product. b. Find the area of the parallelogram in...
linear algebra help 4a. Let It be a non empty subset of a vector space Y,...

linear algebra help 4a. Let It be a non empty subset of a vector space Y, Write the 3 properties for H to be o subspace of y. show that H= 18 9,6 ER a subspace of R4 show that span { v. 7,33} is a subspace of v + 7V2, V E Ve showthat the vegtos (3109) sporno
Hi im struggling with part (b) and (c) of this linear algebra question. Any help would...

Hi im struggling with part (b) and (c) of this linear algebra question. Any help would be greatly apprecated (a) Write down the augmented matrix corresponding to the system of linear equations: + 25 3w W W - + + y y + 1 Na + 4 [2 marks (b) For the remainder of this question the variables v, w, 2, y, and 2 will satisfy a system of linear equations whose augmented matrix is Ab). If the reduced row...

3, (10%) Let V be the subset of R3 consisting of vectors of the form (a,...

3, (10%) Let V be the subset of R3 consisting of vectors of the form (a, b, a). Determine whether V is a subspace of R3. If it is a subspace, give a basis and its dimension